A) \[\frac{(2n)!}{n!}\]
B) \[\frac{(2n)!}{{{(n!)}^{2}}}\]
C) \[\frac{1}{2}\frac{(2n)!}{{{(n!)}^{2}}}\]
D) None of these
Correct Answer: B
Solution :
\[{{(1-2x+3{{x}^{2}}-4{{x}^{3}}+...)}^{-n}}={{[{{(1+x)}^{-2}}]}^{-n}}={{(1+x)}^{2n}}\] \ Coefficient of \[{{x}^{n}}\]in \[{{(1-2x+3{{x}^{2}}-4{{x}^{3}}+...)}^{-n}}\] = Coefficient of \[{{x}^{n}}\]in \[{{(1+x)}^{2n}}={{\,}^{2n}}{{C}_{n}}=\frac{(2n)!}{{{(n!)}^{2}}}\]You need to login to perform this action.
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