decompose-inside-R-x-F-x-x-2n-x-2-1-n-with-n-from-N-and-n-gt-0-

Question Number 30425 by abdo imad last updated on 22/Feb/18

d e c o m p o s e i n s i d e R [x]

F (x) = \frac{x^{2 n}}{{(x^{2} + 1)}^{n}} w i t h n f r o m N a n d n > 0 .

Answered by sma3l2996 last updated on 24/Feb/18

t^{2} = x^{2} + 1

F = \frac{{(t^{2} - 1)}^{n}}{t^{2 n}}

F = {(1 - \frac{1}{t^{2}})}^{n} = \underset{k = 0}{\sum^{n}} C_{n}^{k} {(- \frac{1}{t^{2}})}^{k}

F (x) = \underset{k = 0}{\sum^{n}} C_{n}^{k} {(- \frac{1}{x^{2} + 1})}^{k}