let-give-f-x-1-x-n-1-1-x-n-1-x-n-with-x-R-Z-1-prove-the-existence-of-f-x-2-prove-that-f-is-1-periodic-3-prove-that-f-x-2-f-x-1-2-2f-x-

Question Number 31531 by abdo imad last updated on 09/Mar/18

l e t g i v e f (x) = \frac{1}{x} + \sum_{n = 1}^{\infty} (\frac{1}{x + n} + \frac{1}{x - n}) w i t h x \in R - Z

1) p r o v e t h e e x i s t e n c e o f f (x)

2) p r o v e t h a t f i s 1 - p e r i o d i c

3) p r o v e t h a t f (\frac{x}{2}) + f (\frac{x + 1}{2}) = 2 f (x) .