let-f-x-x-1-2-e-2x-developp-f-at-integr-serie-

Question Number 38726 by maxmathsup by imad last updated on 28/Jun/18

l e t f (x) = \frac{x + 1}{2 + e^{- 2 x}} d e v e l o p p f a t i n t e g r s e r i e .

Commented by math khazana by abdo last updated on 01/Jul/18

f (x) = \frac{1}{2} (x + 1) \frac{1}{1 + (\frac{e^{- 2 x}}{2})} = \frac{1}{2} (x + 1) \sum_{n = 0}^{\infty} \frac{e^{- 2 n x}}{2^{n}}

= \frac{1}{2} (x + 1) \sum_{n = 0}^{\infty} \frac{1}{2^{n}} (\sum_{p = 0}^{\infty} \frac{{(- 2 n x)}^{p}}{p!})

= \frac{1}{2} (x + 1) \sum_{n = 0}^{\infty} \frac{1}{2^{n}} (\sum_{p = 0}^{\infty} \frac{{(- 2 n)}^{p}}{p!} x^{p}) \dots