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)))


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

$W i t h u s u a l n o t a t i o n, s h o w t h a t$ $\frac{C_{0}}{x} - \frac{C_{1}}{x + 1} + \frac{C_{2}}{x + 2} - . . . . + {(- 1)}^{n} \frac{C_{n}}{x + n} =$ $\frac{n!}{x (x + 1) (x + 2) . . . . (x + n)}$
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