Question

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

• A. 4n
• B. 4n-3
• C. 4n+1
• D. None of these

Answer 1

The correct option is A 4n

$[\frac{1+x}{1-x}{]}^2\Rightarrow (1+x{)}^2(1-x{)}^{-2}$

$\Rightarrow (1+x^2+2x)[1+2x+3x^2+...+(n-1)x^{n-2}$

$+n{x}^{n-1}+(n+1)x^n+...]$

coeff of $x^n$ will be given by

(I) When 1 will be multipled by $(n+1)x^n$

(II) When $x^2$ will be multimulied by $(n-1)x^{n-1}$

(III) When 2x will be multiplied by $n{x}^{n-1}$

$\therefore$ coeff. of $x^n=n+1+n-1+2n$

$=4n$

Hence option A