SOLVED: Math Gurus! I need your help!

[Vertimus]

The p-series with p=2 converges to pi^2/6. Can someone please explain me the proof or give me a link to a proof? I'm sure there are thousands of proofs for this equality, but I cannot find any proofs on google (i don't know what to search for).

Thanks.

Note: this is not for homework or any kind of credit. I am asking this question out of curosity.

Clearification: the p series is simply a summation of 1/n^p with respect to n from 1 to infinity. Or simply zeta(p).

SOLVED: this is called the basler problem. Mathworld from wolfram gives three proofs for this.

 

[Vertimus]

bump

 

[JulesMaximus]

Originally posted by: Vertimus
The p-series with p=2 converges to pi^2/6. Can someone please explain me the proof or give me a link to a proof? I'm sure there are thousands of proofs for this equality, but I cannot find any proofs on google (i don't know what to search for).

Thanks.

Note: this is not for homework or any kind of credit. I am asking this question out of curosity.

Clearification: the p series is simply a summation of 1/n^p with respect to n from 1 to infinity. Or simply zeta(p).

Clearification? Dude, that isn't even a word.

 

[Ranger X]

Draw it out and post the JPG.

 

[labrat25]

it's from Fourier series... that's about all i know (never messed with fourier series, just used p series on my last exam)

 

[Kyteland]

From my college calc book:

The exact sum of this series was found by the Swiss mathematician Leonhard Euler (1707-1783) to be
sum(n=1, n=infinity, 1/n^2) = pi^2/6
but the proof of this fact is beyond the scope of this book.

 

[aux]

This is the Basel problem. Try Google again.

 

[Vertimus]

Originally posted by: aux
This is the Basel problem. Try Google again.

I did a search for the riemann zeta function and mathworld (from wolfram) listed it as the basler problem.
This page gives me three proofs.

Thanks for all the help!