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# Rearranging fourier expansion to find solution to a series watch

1. Fourier expansion is

and I'm finding

So at we have

But when gives

Hence

But the issue here is that so I'm not getting the correct series. What am I doing wrong? My brain's dead
2. When n = 2k, then sin(n*pi/2) = sin(k*pi) = 0.

When n = 2k + 1, then sin(n*pi/2) = sin((2k+1)*pi/2) = (-1)^k.
3. (Original post by Glutamic Acid)
When n = 2k, then sin(n*pi/2) = sin(k*pi) = 0.

When n = 2k + 1, then sin(n*pi/2) = sin((2k+1)*pi/2) = (-1)^k.
cheers, taking a second look at the poor sine curve I drew, I now realise I need sleep

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