A) 1
B) \[{{(-1)}^{n}}\]
C) n
D) \[n+1\]
Correct Answer: B
Solution :
We have, \[{{(1+x+{{x}^{2}}+...)}^{-n}}={{[{{(1-x)}^{-1}}]}^{-n}}={{(1-x)}^{n}}\] \[={{\,}^{n}}{{C}_{0}}-{{\,}^{n}}{{C}_{1}}x+{{\,}^{n}}{{C}_{2}}{{x}^{2}}+...+{{(-1)}^{n}}\,{{\,}^{n}}{{C}_{n}}.{{x}^{n}}\] Coefficient of\[{{x}^{n}}\]is\[{{(-1)}^{n}}{{\,}^{n}}{{C}_{n}}={{(-1)}^{n}}\].You need to login to perform this action.
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