Question

If $|x|<1$,then the coefficient of $x^n$ in the expansion of $(1+x+x^2+x^3+....{)}^2$ is

• A. $n$
• B. $n-1$
• C. $n+2$
• D. $n+1$

Answer 1

The correct option is D $n+1$

As $1+x+x^2+x^3+\cdots =(1-x{)}^{-1}$
$\therefore (1+x+x^2+.....{)}^2=(1-x{)}^{-2}$
$=1+2x+3x^2+......$
Therefore, coefficient of $x^n$ is $n+1$.