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## Homework Statement

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)

f(t)=pi-t, -pi<=t<pi

So i need to rearrange this to calc the sum.

## Homework Equations

## 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 don't know how to do this right. I tried replacing with n=2k+1 but it doesn't work.