question_answer

In the expansion of \[{{\left( \frac{1+x}{1-x} \right)}^{2}}\], the coefficient of \[{{x}^{n}}\] will be

A) \[4n\]

B) \[4n-3\]

C) \[4n+1\]

D) None of these

Correct Answer: A

Solution :

Given term can be written as \[{{(1+x)}^{2}}{{(1-x)}^{-2}}\] \[=(1+2x+{{x}^{2}})[1+2x+3{{x}^{2}}+....+(n-1){{x}^{n-2}}\] \[={{x}^{n}}(n+1+2n+n-1)+....\] Therefore coefficient of \[{{x}^{n}}\] is 4n.