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