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# Fourier series watch

1. (This is a past exam paper question that I brought to my tutor today and he couldn't figure it out!)
The first part of the question asks to work out the fourier series for sinh(X). That bit i've done. [Ive included a link here to show the sinh(X) fourier series. this is not my post](https://www.thestudentroom.co.uk/sho...d.php?t=433324)
The next part of the question however is a bit more tricky. it asks to show that 1/(1+1ˆ2) -1/(1+3ˆ2) +1/(1+5ˆ2)-1/(1+7ˆ2) =pi/4cosh( pi/2). I feel like I'm going round in circles attempting this question. I've tried parsevals however nothing in the answer is squared so it doesn't feel like it'd work. Setting x=pi/2 gets a similar series however there is a factor of n missing that I can't work out how to put in unless I integrate? Any way any tips would be greatly appreciated. Thanks!
2. Integrating the sinh series looks like it should work. (Or using the cosh series directly, but since you've already found the sinh one...)
3. (Original post by DFranklin)
Integrating the sinh series looks like it should work. (Or using the cosh series directly, but since you've already found the sinh one...)
looking at it now , integrating it would actually add a factor of 1/n. I'm really hoping that i've just missed a n out of my series somewhere!
4. (Original post by MOH550)
looking at it now , integrating it would actually add a factor of 1/n. I'm really hoping that i've just missed a n out of my series somewhere!
Did you miss that the series in the first post of the thread you linked was incorrect and had a mssing n?
5. (Original post by DFranklin)
Did you miss that the series in the first post of the thread you linked was incorrect and had a mssing n?
No I didn't to be honest. But I also managed to miss out an n in my own calculation which i've now resolved. Thank you very much for the help!

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