question_answer

The coefficient of\[{{x}^{n}}\]in the expansion of \[(1+x){{(1-x)}^{n}}\]is

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 ofin the expansion of = Coefficient ofin + Coefficient ofin