# Combinatorics involving negative rational n in nCr function

Hence, show that

$\frac{1}{\sqrt{1+x} }=\sum_{k=0}^{\infty }\binom{2k}{k}(\frac{-x}{4})^{k} $

## Answer

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Persimmonl

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The answer is accepted.

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Knowledge of the gamma function is not assumed for this question.