# Fourier Series (simple?)

#### nacho

##### Active member
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
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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