Question

The coefficient of $x^{-n}$ in $(1+x{)}^n{(1+\frac{1}{x})}^n$ is

Answer 1

$(1+x{)}^n(1+\frac{1}{x}{)}^n=\frac{(1+x{)}^{2n}}{x^n}$

Coefficient of $x^{-n}$ in $(1+x{)}^n(1+\frac{1}{x}{)}^n$ will be equal to constant term in $(1+x{)}^{2n}$

So the coefficient is ${}^{2n}{C}_0=1$