$\text{ The Coefficient of }{x}^n\text{ in the expression of }(1+x)(1+x{)}^n\text{ is }$

$\begin{array}{l}(1+x)(1+x{)}^n=(1+x)\left({}^{n}C_0+{}^{n}C_{1}x+{}^{n}C_2{x}^2+\dots \dots ..+{}^{n}C_n{x}^n\right)\\ \text{ Coefficient of }{x}^n\text{=}{}^{n}C_n+{}^{n}C_{n-1}\end{array}$

                            $\begin{array}{l}=1+{}^{n}C_1\left(\because {}^{n}C_r={}^{n}C_{n-r}\right)\\ =1+n\end{array}$