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Jet057 asked on 12/09/07 - Question regarding trig identities I have two questions: 1. How do I solve the following? tan^3 x + tan^2 x - 3tanx-3 = 0 ~also~ 2. How do I solve the following? 4sin^2 x + 2cos^2 x = 3 IQGuru answered on 12/10/07: Hi again Jet057! 1: Given: tan^3 x + tan^2 x - 3tanx-3 = 0 Rewrite as: tan^3 x + tan^2 x = 3tanx +3. tan^3 x + tan^2 x = 3(tanx +1). Make left side similar to right side: (tan^2 x)(tanx +1) = 3(tanx +1). Divide out common term: (tan^2 x) = 3. tan x = SqRt3. x = 60 degrees. 2: Given: 4sin^2 x + 2cos^2 x = 3. Rewrite first term: 2sin^2 x + 2sin^2 x + 2cos^2 x = 3. Simplify: 2sin^2 x + 2(sin^2 x + cos^2 x) = 3. 2sin^2 x + 2(1) = 3. 2sin^2 x = 3-2 = 1. sin^2 x = 1/2. sin x = SqRt[1/2] = (SqRt2)/2. x = 45 degrees. Warm regards again, "IQ" Jet057 rated this answer

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lisalisa asked on 08/21/06 - help please ok...i am checking my son homework and of course I dont know the answers so how can I check this. Please help me!!! 1.write a numcerical expression for each of the following (climb up 26 steps, then climb down 9 steps. #2 earn $100, spend $6w, earn $35, spend #72 Find each sum for the following: 1. -8+(-3) = 2. 6+(-6)= 3. -12+ (-17)= 4. 9+(-11)= 5. -4+(-6)= 6. 18 + (-17)= 7. -8+8+(-11)= 8. 12+ (-7) +3+(-8)= 9. -15+7+15= 10. 0+(-11)= 11. 6+(-5)+(-4)+ 12. -5+(-16) +5+8+16= thanks for all of your help!!!!! IQGuru answered on 08/22/06: Hi Lisa! 1. 26steps-9steps=15th step. 2. $100-$6+$35-$72=$57. 1. -8+(-3) = -11 2. 6+(-6)= 0 3. -12+ (-17)= -29 4. 9+(-11)= -2 5. -4+(-6)= -8 6. 18 + (-17)= 1 7. -8+8+(-11)= -11 8. 12+ (-7) +3+(-8)= 0 9. -15+7+15= 7 10. 0+(-11)= -11 11. 6+(-5)+(-4)= -3 12. -5+(-16) +5+8+16= 8 Warm regards, "IQ"

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dawnrich asked on 05/15/06 - what is the day? The day before two days after the day before tomorrow is Saturday. What day is today? IQGuru answered on 06/01/06: Hi! Sorry about the delay answering; I have been away... The day before tomorrow is today. Two days later is the day after tomorrow. The day before that is tomorrow. But that day (tomorrow) is Saturday. So today is Friday. Please RATE all answers you get at Answerway. Warm regards, "IQ"

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Sky-gurl asked on 03/11/06 - Area of a Square What is the arrea of a square if it's perimeter is 56 centimeters? IQGuru answered on 03/12/06: Hi Sky-qurl! If perimeter is 56 centimeters, each side (S) must be S = 56/4 = 14 cm. So Area = S*S = 14cm*14cm = 196 square centimeters. Please RATE any answers you get from me. Warm Regards, "IQ" CeeBee2 rated this answer

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Dathaeus asked on 03/02/06 - hey IQ, trig queries... Hey there how r u... u may be wondering what I am doing here, but I am helping out a friend of mine and my trig is a "bit" rusty.... too much golf and not enough sohcahtoa's in ,my life.... anyways, first, all the stuff about trig id's and laws of sines and cosines basically translate to plug and chug in the high school level correct? I know this is not a fun subject for many students, so were there any tools u used to make it a bit more "interesting" for kids to learn this part of math? Also I have a question about solving for circular arc lengths and lengths of related tangential or incorporated lines with the circle... i'll try to draw or scan a pic if u do not understand me, but hopefully u will, even tho my math lingo may be a bit outdated.... say u have a circle, a very nice symmetric one, and also have two tangential lines outside the circle that intersect... let us label the tangents A and B, and the point of intersection of the two lines C... isnt it true that in the little 2-D conic triangle formed, ACB, the length of AC and CB always have to be the same no matter what, as long as those lines are tangential and non-parallel to each other? I dont remember how u prove that, is it law of cosines? but I am asking intuitively here because that is what it seems... And thirdly, in general, how are these two different types of problems handled differently.... one where a circle is given and the lines given are outside the circle, and we need to solve for arc lengths or included angles, etc... as opposed to if in a circle, the lines given are INSIDE the circle and we need to find out similar info... what is the general approach for each, or depending in the problem does it have to be a mixture between the trig id's and circular segment formulae? Thanks! IQGuru answered on 03/03/06: Hi Datheus! Re your first qustion: Please READ the trig course I have posted on your site. My tricks, tools, and especially the shortcuts are ALL there!... Re your 2nd question: Yes, the lengths of both tangents to a circle from any outside paint are always equal. This is Geometry Theorem #10. Its proof is to draw lines from points of tangency to circle center and from the point of intersection to circle center --this always create two identical right triangles... Re your 3rd question: You should first use (are first using) Geometry IDs, not Trig IDs, for such problems. (Trig is the study of triangles, not circles.) So the approach to both problems is to first convert it to triangles with Geometry, and then to solve the triangles found with either more geoemetry or with Trig, as may be easiest in each case. Warm regards, "IQ" Dathaeus rated this answer

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z298418 asked on 01/04/06 - Commitment Hello, How do you answer to this question? Please give examples of ways you have planned or achieved results in a work and/or military environment. thank you for your time. IQGuru answered on 01/04/06: Hi there! Your question seeks to find out how much initiative you demonstrate at work, to the benefit of the organization, as a result of your own ideas or planning. The question is twofold: If you held a management position, it seeks to determine insight into how you plan AND execute actions; if you held only lower positions, it seeks to determine what improvements you brought to the organization by being there, through your own suggestions and ideas. Example: When I was a Seaman Apprentice (definitely a low position) assigned for several weeks to help clean Navy galley kitchen floors, I soon noticed than all the galley cooks were growling about the unkept nature of the condiments and spice pantry. The pantry was a 6' x 6' room, 7' high with one 60 watt ceiling light, and with small floor-to-ceiling shelving on all available walls (even above the door) and was in a state of complete mess and disorder. So I asked the galley supervisor if I could (tomorrow) clean and reorganize the pantry instead of cleaning floors. He was delighted with that idea! That evening I went to a store and bought one set of stick-on paper alphabet and one 100 watt lightbulb. The next day, I first replaced the pantry 60W with my 100W so one could see better in there. Then I emptied the pantry into piles outside its door, completely cleaned the shelving and floor, and began its reorganization by placing an 'A' sticker on the higest shelf edge to the immediate left of the door. I then found all condiments and spices (from my piles) which began with the letter 'A', and arranged those ALPHABETICALLY onto shelves of the 'A' section, cleaning each item as it was stored. Then, after leaveing a bit of space for new items, I repeated this process for 'B' and each subseguent letter on shelves around the room. At the end of the day, the pantry and each item therein was sparkiing clean under the new brighter light, and every item was in easy-to-find alphabetical order. The supervisor also immediately observed that the shelf labeling would tend to 'force' cooks to replace items in more proper places, thus both avoiding future misplacement or loss of items in the pantry and making needed reorders easier to indentify, and greatly increasing the efficiency of his entire cooking staff by reducing wasted time searching for things in the pantry... Got the idea? CeeBee2 rated this answer z298418 rated this answer

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peggym2010 asked on 12/19/05 - Runs 800 ft algebra1 ok Mariko runs 800ft in one min. what is her approximate speed in miles per an hour? (hint: 5280ft=1mi. IQGuru answered on 12/20/05: Hi Peggy! (800feet/min)*(1 mile/5280 feet)*(60min/hour) = 9.09091 miles/hour Warm regards, "IQ"

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z298418 asked on 10/10/05 - Make it short Would you please tell me what is they talk about here short answer please, and In English please. Postmodernism is not so much a theoretical construct as Marxism is but rather a philosophical excursion or viewpoint of current though and expression. The role of language is that of providing a cultural base for expression. These view points and philosophies are expressed in these languages but are not guided by them. Thus the philosophy may add to the structure and development of the language but does not form the foundation there of. IQGuru answered on 10/13/05: Hi! Postmodernism is a way of looking at things rather than a defined doctrine. Laguage allows the expression of philosophy. Such expressions may lead to the invention of new words. This does NOT mean that philosophy causes language itself to develop. z298418 rated this answer

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z298418 asked on 07/09/05 - proff reading proof reading proof reading would you please proof reading my essay my proffsor told me I need more details. I not sure what she mean by that. thank you for your help. “Being Successful in America” What does it mean to be “successful” in America? Many people from different countries come to the United States to find a better life and more opportunities to have success that in their countries can’t be found. Some people want to have success in their career or in their family, but other people think money is the most important because they can buy a luxury houses, wonderful cars and live like a rich person. In the essay “ The Way to Wealth” the author Franklin describes his own vision about having success in life. In my own definition of success, I think I need to achieve in many different areas such as education, career, family and health. Since I came to America from Italy in 2002, I have believed that education is very important to have success in life. Education is a key point because it can open someone to possibilities and more opportunities to find a good job with benefits and earn a lot of money. When I came to the United States, I already had my accountant diploma and I thought “ I can have many opportunities to find a job for what I had studied at school than I couldn’t have in Italy” ; but I was wrong. In America there is a different education system and I need to take the same subjects I did in Italy but this time in the English language because my diploma is not valid here. I realized that, when for the first time, I applied for a job as an accountant. The company refused my application and they didn’t hire me because my education was too poor for them. After, this experience I realized I needed to go to school again. I have decided to refocus my education from accounting to culinary arts; and I have learned that having a college degree in America will be the key to have more opportunity for the future. Education is important because it can help everybody to a new world of knowledge. If someone goes to school and achieves a degree, he or she can learn many things and have the opportunities to find a good job. I believe education can lead me to find my dream job. My dream job is one day be a chef because I like to cook and bake different foods. Since I studied at Manchester Community College in Hospitality Management, I found very interesting the classes and every semester I have learned something new. In Italy, I never had the opportunity to study in this field and what I knew and learned, it’s always new from baking to cooking preparation. For almost two years, I didn’t find a job as an accountant and after my exhaustion, I choose to work in the factory, even I didn’t like it. I worked in the factory because I need money and I didn’t want to stay all day at home and doing nothing. Here, in America, with all my skills in Hospitality Industry, I want to open my own bakery. I want to try my ability and my capacity to run a business. Also, I want to see the people’s faces when they buy my products. Also, family is important to have success in life. When I dreamed to be a chef my parents didn’t support me financially and emotionally my decision because they thought if I was an accountant I could find a secure and fast job everywhere, but it wasn’t as they thought. Even though my husband, like my parents, doesn’t accept my decision to be a chef, he supports and encourages me a lot. He doesn’t like my decision because he thought it’s a hard work, always standing up for many hours, always work on Saturday and on Sunday and even the holiday season. In addition, being a chef doesn’t pay much money. I always told him that money for me is not very important (yes, it’s counts) but more important is what I love to do. However, he encourages me to go to school again to pursue my dream. In addition, he believes in my capacity, even though he knows for me its will be difficult, in the new country with new language to learn and understand, the American’s lifestyle and the people. During the past two semesters at Manchester Community College, he supports me a lot financially and emotionally. When I’m going to school in the morning, he took care of our fourteen months old daughter and then when I came back home, he goes to work. In fact, he still does the same thing now during my summer class. If I couldn’t have my husband’ help, I couldn’t go to school and have the opportunity to learn something new in my life. Family is important in our society because supports, helps and understands you in difficult situation and never leave you. Another important key to have success in life is health. In the morning, I’m going to school and when I came back home in the afternoon I take care of my fourteen months old daughter and I need to stay healthy. Right now, I fell very tired and exhausted because I’m pregnant and it’s difficult to combine school and family together. Being a pregnant woman, I need to eat healthy foods, don’t lift heavy things, take vitamins but at the same time I need to take care of my daughter and my husband. Even my daughter is so small, it’s very stressful to follow her: where she goes, what she puts in her mouth, and what she eats and touches. Always I need to stay ready and watch her all the time. In fact, I do my homework when she goes to bed or she plays alone with her toys. Stay healthy and eat foods are very important because if you feel bad or sad you can’t pursue what you dream. Finally, when you have a stable family who support and help you in the difficult situation, you can pursue whatever you want in your life such as go to school and have a good education for find a job. However, in order to realized your accomplishment you need to stay healthy. Most people from different countries come to the United States and they find their success. IQGuru answered on 07/09/05: Dear z298418: I hae no real way to determine exactly what type of 'details' your professor had in mind -- you need to ask that professor that question -- except for the glaring problem in your first paragraph: Your reference to Franklin needs to be either eliminated or contrasted to your own ideas, because you statement that he had some ideas too (so did/does everybody else!) just leaves the reader wondering why you bothered to mentioned him in particular, or at all... Otherwise, I cannot guess what else your professor may have had in mind. I could correct your grammar here, if needed, but that is not what you asked for. So if you need that too, please ask by followup. But I have no other ideas concerning what your professor may have been thinking about. Warm regards, "IQ" excon rated this answer z298418 rated this answer

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5incere asked on 04/14/05 - rapid estimation 1. estimate the number of munutes in a human lifetime assumptions: plan(sketch,equationsto be used, etc) - - - - - - 1. estimate the number of students at your high-school assumptions: plan(sketch,equationsto be used, etc) - - - - - - 1. estimate the number of tennis balls that would fit in a classroom assumptions: plan(sketch,equationsto be used, etc) - - - - - - IQGuru answered on 04/15/05: Hi again, Sincere! First, thanks for all the stars on my previous answers! Second, here are some ideas for your new set of questions: (1) Including leap years, the average length of a year is 365 1/4 days. Therefore: (60 minutes/hr)*(24hr/day)*(365.25 day/yr)=526,320 minutes/year... A reasonable 'roundoff factor' here might be 526,000, 525,000, or 500,000 min/yr, dependent upon what level of accuracy you seek. The only other real 'estimate' necessary here is the avearage life of a human, which varies greatly from country to country. You could find estimates of this from various sources -- such as actuarial tables. I would 'estimate' using both 60 and 80 years, using 500,000 mins/year. That way, you can do the multiplications in your head, and your result will give a good range: Between 30,000,000 and 40,000,000 minutes, i.e., between 30 and 40 million minutes. (2) (Average Number of Students/Class)* (Average Number of Classes/Grade)* (Number of Grades in this Highschool). Just make reasonable assumptions about the average values used. In my (large) highschool, the above would have been about 30*16*3 = 1448. (3) A tube of 4 tennis balls is about a foot long, so a square foot of tennis ball tubes (4 tubes) would be 16 balls and a cubic foot of tennis ball tubes (16 tubes) would be 64 balls. Removing the balls from the tubes would allow denser packing, so you might estimate about 70 balls per cubic foot. So estimate length, width, and height of your classroom (in feet) and multiply that product by 70. For example, if the classroom is 40'x50'x7', your answer would be 40*50*7*70 = 980,000 balls. Comments are welcome, as always. Warm regards, "IQ" 5incere rated this answer

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lyc123 asked on 10/15/04 - unit vectors In this question, i is a unit vector due east and j is a unit vector due north. An aircraft is flying directly from A to B, which is 2000km from A. The velocity in still air of the aircraft is (150i+50j)km/h and the ground speed is (200i-30j)km/h. Calculate (i) the time of flight, to the nearest min. (ii) The direction of the wind. IQGuru answered on 10/16/04: Hi again, lyc123! I shall give you a lot of detail here, just in case you want to really see what is going on... The still air velocity would look like this: (Ignore doted lines, which are used for spacing here.) .............B A______| +50j ...+150i [I cannot draw line AB here; please add that yourself.] Notice that the two vectors have a ratio of 50 times [3:1]. So, by pythagorus, side AB must be 50*[SgRt(9+1)], i.e., 50*SqRt[10], or about 158.114 km/hr, toward East of Northeast. Thus, if the air were still (it isn't) the trip from A to B would take: 2000km/(50SqRt10km/hr) = 40hr/SqRt10 = 12.649 hours. But the actual velocity (groundspeed) looks like this: ......+200i A________ ................| -30j ................B' [Again, please add line AB' yourself.] Notice that these two vectors have a ratio of 10 times [20:3]. So, by pythagorus, side AB' must be 10*[SgRt(400+9)], i.e., 10*SqRt[409], or about 202.237 km/hr, toward East of Southeast. The above shows that the plane gets a 80 km/hr 'kick' toward SOUTH from the wind, and a 50 km/hr 'kick' toward EAST from the wind. So. to COMPENSATE for the wind, the plane would have to 'aim' its flight somewhat NORTHWEST of where B actually is, as if it were flying somewhere else!... But regardless of that 'apparent' direction or aiming, the distance actually flown still must be 2000 km. The ACTUAL flight time is thus: 2000km/(10SqRt409km/hr) = (200hr/SqRt409)*(60min/hr) = 12000min/SqRt409 = 593.36 min = ~ 9hr, 43 minutes. From all above, it should also be obvious that the wind has velocity components of +50i and -80j. So the wind vectors look like this: +50i C_ ....| -80j ....| ....D [Again, please add line CD yourself.] Notice that these two vectors have a ratio of 10 times [5:8]. So, by pythagorus, side CD must be 10*[SgRt(25+64)], i.e., 10*SqRt[89], or about 94.340 km/hr, toward South of Southeast. The direction of CD (the wind) is thus +50i,-80j, and/or (same as) +5i,-8j, toward South of Southeast. {Compass direction here is 90+ArcTan(8/5)= ~ 147.995 degrees.) Hope all this makes everything clear to you! Warm regards, "IQ" lyc123 rated this answer

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ROLCAM asked on 11/05/03 - Mathematics for Adults!! This category has been very dormant lately. To stir things up a little. What would be " Three Mysterious Numbers in Mathematics". Best wishes,always. ROLCAM. IQGuru answered on 11/05/03: Pi, e, and i. If you want to have a discussion, I suggest you use the subject Forum instead of the subject Question Board. "IQ" ROLCAM rated this answer

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cy_ced asked on 04/13/03 - Question Are you psychic or do readings? IQGuru answered on 04/14/03: I refuse to over-classify myself by any of the currently or popularly accepted definitions of 'psychic', so in that sense my answer must be 'no' to both of your questions. Please let me explain: A better (but still imperfect) classification for me might be 'empathic'. If I can hold your hand, I might (might not) obtain flashes of insight about you. I have no absolute control over whether I do or do not; when it happens, it happens. Furthermore, I do not believe that ANYBODY can do such things 'at will', or on a telephone line, or on the internet, or at this site. Instead I believe that anybody who says they can is either self-delusional - or a fraud. "IQ" cy_ced rated this answer

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hyperdrome asked on 03/30/03 - The Development of Quality Practices since 1940s. Dear IQGuru, Can you please help me with this essay topic: "Describe the developments of quality practices in business with particular reference to the role of information technologies." I need to Commence my discussion from the beginnings of information science in the 1940s. I completely don't understand the topic, so if you could please guide me in the right direction and how should i go about setting the layout of this essay. Sorry about this, but i has been a while since i wrote an essay. Thank you so much for your time. Kind regards, Dee IQGuru answered on 03/30/03: Dee: I am not sure I understand your assignment and fear I can offer little help. In general, quality-control and stress analysis has moved from eye inspection to x-ray and neutron molecular inspection. Meanwhile, the determination of necessary sample sizes for statistical analysis - which once required mathematicians on staff -is now done with hand-caluculators on the production floor. All of these functions have been impacted by increased availability of computer technology and the ever-increasing speed of its transmission, both at lower cost. A consumer in Cairo Eqypt can now have a 'free' MSN-messenger conversation with a salesman or floor manager in Buffalo NY. All of these factors now influence when, how, and how often quality is monitored. "IQ" hyperdrome rated this answer

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craigchamberlain asked on 01/16/03 - follow up question Hi IQGuru, you sent me a follow up question about slow server but when I clicked it on it took me to the home page but said I didn't have any new questions,so I don't know what you asked me. thanks, craig IQGuru answered on 01/16/03: Hi Craig! Well, sorta. What I actually tried to do was add a rather long followup/clarification question to your question, which you had posted on the Networks board. But I found that question indirectly, on the Home page Public board (not directly on the Networks board) so I added my comment from that Public board (twice) so that both your prior answerers (ScottGem and VoiceGuy) might then expound upon it. That seemed to be fine, yesterday; my comment was at that time displayed there twice. But overnight, your question fell off the Public board, and my comments have disappeared! I do not know if that is the way things are supposed to work, or if that is a glitch. Meantime, sorry about all the confusion I created here! Anyhow, the crux of my prior comment was as follows: I too am in a remote area, with only two choices for ISP. I use the faster one! But even there, with 56K modem dialup, the fastest speed I can normally get is 44,000 bps. In that situation, I have found the addition of 'accelerators' helpful; but I do not know if they would similarly help you where the maximum seems to be 29,000 bps, which is what I wanted you to ask Scott and Voiceguy about... as well as whether they thought accelerators would be worth the expense and/or bother to you... You still need to ask them that, based upon the below. I use both the 'Netsonic' and the 'Internet Boost' accelerators, at the same time! This gives me an 'effective' speed which is actually faster than 56K, for all practical purposes; i.e., about 77,332 bps. But there are downsides: First, these two particular accelerators were NOT designed to work with each other, or with any other. So I had to make extensive modifications to BOTH programs, to make that work. (Should you happen to someday choose those same two accelerators, I would be happy to share the details...) There are lots of accelerators on the market, which I know nothing about; the two I use cost about $35 each... Second, my Netsonic accelerator requires the creation of an additional memory cache, which eats memory, and which also must be purged VERY often. (Many times a day). Nonetheless, personally, I find this effort worthwhile, in order to achieve cable-like speeds with my meager 56K modem. I do not know if you would find it equally gratifying; you might view the 4 clicks necessary to constantly purge that cache a pain in the ... Third, if you do 'stack' accelerators, you will have to do some experimentation to determine where you actually have the fastest speeds, because both of the stacked accelerators will lie, because they are stacked, and because logic will not work there! For example, I repeatedly logoff/on to my ISP until it gives me a connection speed of 38,666 pbs, because my 'stack' will operate faster there than it will if the ISP gives me 44,000 bps! OK, now you know what I know; please feel free to copy any portion of this with your mouse, and/or ask Scott and Voiceguy about it; they know much more about such things that I do, and can probably better advise you whether an accelerator would help you, in your particular situation. Warm regards, "IQ" craigchamberlain rated this answer

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zoomk1 asked on 11/03/02 - induction C(n,0)-C(n,1)+C(n,2)+or-...C(n,n)=0 also written as: the sum of i=0 to n and (-1)^i*[C(n,i)]=0 since i need to prove it with a negative, im having a really,really difficult time. i can do one without a negative: example:sum of i=0 to n and C(n,i)=2^n, this doesnt have a negative.In the problem where it states the sum, i mean to put the summation sign if that confuses you at all.nobody else has been able to really help me out, if you can help me out at all with this one it will be greattttly appreciated, thankyou :) IQGuru answered on 11/08/02: THIS IS A DUPLICATE QUESTION! Hi! Merely move all the negative terms to the right side of the equation and look at it: C(n,0)-C(n,1)+C(n,2)+or-...C(n,n)=0. C(n,0)+C(n,2)+C(n,4)+...=C(n,1)+C(n,3)+C(n,5)+... C[(n,0)+(n,2)+(n,4)+...]=C[(n,1)+(n,3)+(n,5)+...]. (n,0)+(n,2)+(n,4)+...=(n,1)+(n,3)+(n,5)+... Thus, by induction, this equation can only be true if n=0, or if n=infinity; n=infinity is a trivial solution. Thus n=0. Warm regards, "IQ"

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zoomk1 asked on 11/03/02 - induction C(n,0)-C(n,1)+C(n,2)+or-...C(n,n)=0 also written as: the sum of i=0 to n and (-1)^i*[C(n,i)]=0 since i need to prove it with a negative, im having a really,really difficult time. i can do one without a negative: example:sum of i=0 to n and C(n,i)=2^n, this doesnt have a negative.In the problem where it states the sum, i mean to put the summation sign if that confuses you at all.nobody else has been able to really help me out, if you can help me out at all with this one it will be greattttly appreciated, thankyou :) IQGuru answered on 11/08/02: Hi! Merely move all the negative terms to the right side of the equation and look at it: C(n,0)-C(n,1)+C(n,2)+or-...C(n,n)=0. C(n,0)+C(n,2)+C(n,4)+...=C(n,1)+C(n,3)+C(n,5)+... C[(n,0)+(n,2)+(n,4)+...]=C[(n,1)+(n,3)+(n,5)+...]. (n,0)+(n,2)+(n,4)+...=(n,1)+(n,3)+(n,5)+... Thus, by induction, this equation can only be true if n=0, or if n=infinity; n=infinity is a trivial solution. Thus n=0. Warm regards, "IQ"