A) \[{{(-1)}^{n-1}}n\]
B) \[{{(-1)}^{n}}(1-n)\]
C) \[{{(-1)}^{n-1}}{{(n-1)}^{2}}\]
D) \[(n-1)\]
Correct Answer: B
Solution :
Coefficient of \[{{x}^{n}}\] in expansion of \[(1+x)\] \[{{(1-x)}^{n}}\] ie., coefficient of \[{{x}^{n}}\] in expansion of \[{{(1-x)}^{n}}+\] coefficient of \[{{x}^{n-1}}\] in expansion of \[{{(1-x)}^{n}}\] Now, \[{{(-1)}^{n}}{{\,}^{n}}{{C}_{n}}+{{(-1)}^{n-1}}\,{{\,}^{n}}{{C}_{n-1}}\] \[{{(-1)}^{n}}\,{{[}^{n}}{{C}_{n}}-{{\,}^{n}}{{C}_{n-1}}]\] = \[{{(-1)}^{n}}\,[1-n]\].
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