<p>Dont waste too much time, it’s a lame question… hehe.
Try finding the sum - 1/1^2 + 1/2^2 + 1/3^2 … + 1/n^2</p>
<p>This board is in desperate need of TeX :)</p>
<p>ok mercurysquad. Firstly, well done. U gave an ecellent answer to my question. Second, for your 2 questions i think they r really interesting and i am still workin’ on them. Meanwhile u can work on this. There are two cities, one with habitants that only lie and the other with habitants that only tell the truth. you are in one of the 2 cities but u dont know which one and u are allowed to make only one question to understand in which city u are. what is that question?(the question should be related to the clues, because there are infinitely many solution like, what is the derivate of 2X^2. the liers would say anything except 4X and you would know they are the liers, instead the honest would emediatey say 4x)</p>
<p>Sorry I missed this thread long back.
As for answer to the ant question - it’s a moronic question, sorry 
The answer is - the middle ant is lying ;)</p>
<p>For the sum of the series: there is no closed form solution. Just google and you will find out why. I was asked this question by my physics teacher when he found out I was taking engineering prep classes outside school. I couldn’t solve it and he made fun of me!</p>
<p>Now for your riddle about the two cities - </p>
<p>Ok, my question to an inhabitant of the city would be - “Are you going to answer this question?”</p>
<p>Truth city guy will say yes. Can’t say no, because by that time he would have answered it.</p>
<p>Liar city guy will say no. Can’t say yes, because that would be the correct answer but he has to lie.</p>
<p>Since you people are in the mood for riddles and weird problems, did you know about the 3n+1 problem? <a href=“"The 3n+1 problem" - Google Search”>"The 3n+1 problem" - Google Search; (the first 3 links are the most relevant)</p>
<p>for the riddle of the two cities the question is quite straightforward. You ask an inhabitant: “Are you from this city?”
The liar would say no and the one who says the truth will say yes.
This problem actually originates from a russian math olympiad.
As for your problem mercurysquad:</p>
<p>1/1^2 + 1/2^2 + 1/3^2 … + 1/n^2…=zeta(2)=pi^2/6
There are many proofs for this but they are a bit complicated</p>
<p>o dele po pse ju pergjigje pytjes time(ne te vertet tates po nejse) me kar. Persa i perket vragut, je i sigurt qe eshte ashtu?</p>
<p>TemplarOfSteel, could you please elaborate on the solution, because your answer is pi^2/6 but the left hand side is not an infinite series. I asked for the sum of the series as a function of ‘n’ … your solution is constant for any n unless I’m missing something obvious here…</p>
<p>And for the 3n+1 problem, we worked on that for my Symbolic software lab course this semester. There is no proof so far, but we used numerical methods to prove it for all n upto some integer, say, 1000. And the graph of the 3n+1 numbers is pretty interesting too… almost random.</p>
<p>i’m quite sure you can not find the sum for any n. Do you have a solution mercurysquad? by the way the most interesting unsolved problem imo is p versus np</p>
<p>no, templarofsteel, i don’t have the solution. you’re right, you cant find it for any n != infinity. back in high school i didnt understand why, and i still don’t understand fully… all i know is this is a nice trick to play on anyone, because it seems like a simple GP/AP problem.</p>