A) \[^{m+n}{{C}_{m-1}}\]
B) \[^{m+n}{{C}_{n}}\]
C) \[^{m+n}{{C}_{m-n}}\]
D) None of these
Correct Answer: B
Solution :
We have, \[{{(1+x)}^{m}}{{\left( 1+\frac{1}{x} \right)}^{n}}={{(1+x)}^{m}}{{\left( \frac{x+1}{x} \right)}^{n}}\] \[=\frac{{{(1+x)}^{m+n}}}{{{x}^{n}}}={{x}^{-n}}(1+x{{0}^{m+n}}\] \[\therefore \]Required term independent of\[x\] = Coefficient of\[{{x}^{0}}\]in\[{{x}^{-n}}{{(1+x)}^{m+n}}\] = Coefficient of\[{{x}^{n}}\]in\[{{(1+x)}^{m+n}}\] \[{{=}^{m+n}}{{C}_{n}}\]
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