The term independent of x in the expansion of 1-xn1-1-xn is -

The correct option is D (1 + x)^n (1 + 1/x)^n = nbsp; (1+x)^2n/x^n Term independent of x in (1 + x)^n(1 + 1/x)^n is coefficient of x^n in (1 + x)^2n = nbs ...

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Byju's Answer

Standard XII

Mathematics

Sum of Product of Binomial Coefficients

The term inde...

Question

The term independent of x in the expansion of $(1 + x)^{n} (1 + \frac{1}{x})^{n}$ is :

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Solution

The correct option is C

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

Term independent of x in $(1 + x)^{n} (1 + \frac{1}{x})^{n}$ is coefficient of $x^{n}$ in $(1 + x)^{2 n}$

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

But we know that $C_{0}^{2} + C_{1}^{2} + C_{2}^{2} + . . . . . . . . . . . . + C_{n}^{2} =^{2 n} C_{n}$

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The term independent of x in the expansion of (1+x)n(1+1x)n is :

The correct option is C (1+x)n(1+1x)n=(1+x)2nxn Term independent of x in (1+x)n(1+1x)n is coefficient of xn in (1+x)2n = 2nCn But we know that C20+C21+C22+............+C2n=2nCn

The term independent of x in the expansion of $(1 + x)^{n} (1 + \frac{1}{x})^{n}$ is :