The term independent of x in (1+x)m1+1xn, is - Infinity Learn by Sri Chaitanya

$Given, (1 + x)^{m} \cdot {(1 + \frac{1}{x})}^{n}$

To find Term independent of x

coefficient of x⁰ in $\{(1 + x)^{m} \cdot {(\frac{x + 1}{x})}^{n}\}$

$\Rightarrow$ coefficient of x⁰ in $\{\frac{(1 + x)^{m + n}}{x^{n}}\}$

$\Rightarrow$ Coefficient of xⁿ in $(1 + x)^{m + n}$

$\Rightarrow$ Coefficient of xⁿ in $\{^{m + n} C_{r} x^{r}\}$

$\Rightarrow^{m + n} C_{n}, put r = n$

.'. Term independent of. x $=^{m + n} C_{n} {or}^{m + n} C_{m}$

The term independent of x in $(1 + x)^{m} {(1 + \frac{1}{x})}^{n}, is$