Studying for an exam, this is a question from an earlier exam:
Calculate: sum k from 1 to infinity, 1/k^2
I have from previous question:
f(t)=pi+sum n from 1 to infinity: 2*(-1)^n/n*sin(nt)
So i need to rearrange this to calc the sum.
The Attempt at a Solution
calc f(t) in a good point, I choose pi/2, use the left and right limit to get pi/2
then try top rearrange the series.
Especially I want to know mhow to do Sin(n*pi/2). it makes every second term disappear in the series but I dont know how to do this right. I tried replacing with n=2k+1 but it doesnt work.