Coefficient of 1x in the expansion of (1+x)n(1+1/x)n is

We have (1+x)n1+1xn=(1+x)2nxn ∴ Coefficient of xn−1 in (1+x)2n=2nCn−1

Coefficient of 1x in the expansion of (1+x)n(1+1/x)n is

We have (1+x)n1+1xn=(1+x)2nxn ∴ Coefficient of xn−1 in (1+x)2n=2nCn−1

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Coefficient of $\frac{1}{x}$ in the expansion of $(1 + x)^{n} (1 + 1 / x)^{n}$ is

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$^{2 n} C_{n - 1}$

$^{2 n} C_{n}$

answer is A.

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Detailed Solution

We have

$(1 + x)^{n} {(1 + \frac{1}{x})}^{n} = \frac{(1 + x)^{2 n}}{x^{n}}$

$∴$ Coefficient of $x^{n - 1}$ in $(1 + x)^{2 n}$

$=^{2 n} C_{n - 1}$

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Coefficient of 1x in the expansion of (1+x)n(1+1/x)n is

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Coefficient of $\frac{1}{x}$ in the expansion of $(1 + x)^{n} (1 + 1 / x)^{n}$ is