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Fourier Series (simple?)

nacho

Active member
Sep 10, 2013
156
Is there some properties I should be aware of?

after making the relevant substitutions, I ended up with

$2 = 1 + \sum\nolimits_{m=0}^\infty \frac{4}{(2m+1)\pi}\sin(\frac{(2m+1)\pi}{2})$

but I can't get past this
 

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zzephod

Well-known member
Feb 3, 2013
134
Is there some properties I should be aware of?

after making the relevant substitutions, I ended up with

$2 = 1 + \sum\nolimits_{m=0}^\infty \frac{4}{(2m+1)\pi}\sin(\frac{(2m+1)\pi}{2})$

but I can't get past this
Rearrange to:

\(\displaystyle \frac{\pi}{4}=\sum_{m=0}^\infty \frac{1}{2m+1}\sin\left(\frac{(2m+1)\pi}{2}\right)\)

and ask yourself what values does the sine of odd half multiples of \(\displaystyle \pi \) take?

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