I need to sum 1/n^2, n=1 to infinity

Question

zzr0ck3r · Answer

not to easy

zzr0ck3r · Answer

http://en.wikipedia.org/wiki/Basel_problem

kainui · Answer

http://math.stackexchange.com/questions/183316/how-to-get-to-the-formula-for-the-sum-of-squares-of-first-n-numbers So if you scroll down a little there's a nice derivation of the formula. Anything that you don't understand I can explain but at the very top there's the formula n(n+1)(2n+1)/6 where n is the highest number.

kainui · Answer

Of course you need to plug in 1/n for n into the formula to make it work since your problem is only slightly different.

zzr0ck3r · Answer

you can find many proofs on the internet, pick one that makes since to you. If you know the expansion of sin(x) I would suggest using that one....

kainui · Answer

Yeah I'm pretty sure my method isn't going to work out haha.

anonymous · Answer

This may be it, but im still looking

kainui · Answer

Yes, it's a well known result that it is pi^2/6 and I first saw it with the power series of sinx divided by x equated with another infinite sum. Pretty cool.

anonymous · Answer

http://www.wolframalpha.com/input/?i=sum+1%2Fn^2%2C+n%3D1+to+infinity