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Question Number 33980 by abdo imad last updated on 28/Apr/18

1) l e t c o n s i d e r f (x) =∣ c o s x ∣ π p e r i o d i x

d e v e l o p p f a t f o u r i e r s e r i e

2) f i n d t h e v a l u e o f \sum_{n = 1}^{\infty} \frac{{(- 1)}^{n}}{4 n^{2} - 1}

3) f i n d t h e v a l u e o f \sum_{n = 1}^{\infty} \frac{1}{{(4 n^{2} - 1)}^{2}} .