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Q.
The term independent of $x$ in $(1+x)^{m}\left(1+\frac{1}{x}\right)^{n}$ is
Binomial Theorem
Solution:
We have,
$(1+x)^{m}\left(1+\frac{1}{x}\right)^{n}=(1+x)^{m}\left(\frac{x+1}{x}\right)^{n}$
$=\frac{(1+x)^{m+n}}{x^{n}}=x^{-n}(1+x)^{m+n}$
$\therefore $ Required term independent of $x=$ coefficient of $x^{0}$ in
$x^{-n}(1+x)^{m+n}=\text { coefficient of } x^{n} \text { in }(1+x)^{m+n} $
$={ }^{m+n} C_{n}$