With-usual-notation-show-that-C-0-x-C-1-x-1-C-2-x-2-1-n-C-n-x-n-n-x-x-1-x-2-x-n-

Question Number 22640 by Tinkutara last updated on 21/Oct/17

W i t h u s u a l n o t a t i o n, s h o w t h a t

\frac{C_{0}}{x} - \frac{C_{1}}{x + 1} + \frac{C_{2}}{x + 2} - \dots . + {(- 1)}^{n} \frac{C_{n}}{x + n} =

\frac{n!}{x (x + 1) (x + 2) \dots . (x + n)}