- #1
maddogtheman
- 18
- 0
Use the Fourier series technique to show that the following series sum to the quantities shown:
1+1/3^2+1/5^2+...+1/n^2=pi^2/8 for n going to infinity
I foudn the series to be:
sum(1/(2n-1)^2,n,1,infinity)
but I don't know how to prove the idenity.
I don't know how to go about solving it using the Fourier method. Any help would be greatly appreciated, thanks!
I was able to prove sum(1/n^4,n,1,infinity)=pi^4/90 and sum(1/n^2,n,1,infinity)=pi^2/6 and I'm not sure if the problem is simular.
1+1/3^2+1/5^2+...+1/n^2=pi^2/8 for n going to infinity
I foudn the series to be:
sum(1/(2n-1)^2,n,1,infinity)
but I don't know how to prove the idenity.
I don't know how to go about solving it using the Fourier method. Any help would be greatly appreciated, thanks!
I was able to prove sum(1/n^4,n,1,infinity)=pi^4/90 and sum(1/n^2,n,1,infinity)=pi^2/6 and I'm not sure if the problem is simular.