Find the coefficient of $x^n$ in the expansion of $(1+x) (1- x)^n$.

#### Solution

Coefficient of $x^n$ in $(1+x) (1- x)^n$
$=$ Coefficient of $x^n$ in $(1-x)^n$ $+$ Coefficient of $x^{n-1}$in $(1-x) ^n$
$= (-1)^n$ $^nC_n$  +$(-1) ^{n-1}$ $^nC_{n-1}$
$=(-1) ^n (1-n)$