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Question Number 28826 by abdo imad last updated on 30/Jan/18

l e t g i v e f (x) = e^{- x} c o s x a n d 2 π p e r i o d i c

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

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