Question

Find the term independent of x in $(1+x{)}^m$ ${(1+\frac{1}{x})}^n$

Answer 1

Given that $\begin{array}{c}{\left(1+x\right)}^m{\left(1+\frac{1}{x}\right)}^n\\ Now,\\ \frac{{\left(1+x\right)}^{m+n}}{x^n}\end{array}$

For independent term of $x$.

Coefficient of $x^n$ in ${\left(1+x\right)}^{m+n}$

Hence, term independent of $x={}^{m+n}{C}_n$