A) \[(n-1)\]
B) \[{{(-1)}^{n}}(1-n)\]
C) \[{{(-1)}^{n-1}}{{(n-1)}^{2}}\]
D) \[{{(-1)}^{n-1}}n\]
Correct Answer: B
Solution :
The coefficient of\[{{x}^{n}}\]in the expansion of\[(1+x){{(1-x)}^{n}}\] = coefficient of\[{{x}^{n}}+\]coefficient of\[{{x}^{n-1}}\] \[={{(-1)}^{n}}\frac{n!}{n!10!}+{{(-1)}^{n-1}}\frac{n!}{1!(n-1)!}\] \[={{(-1)}^{n}}\left( \frac{n!}{n!0!}-\frac{n!}{1!(n-1)!} \right)\] \[={{(-1)}^{n}}(1-n)\]
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