Coefficient of 1x in the expansion of 1-xn 1-1-x n is

The correct option is A 2n!/n 1!n+1! Simplifying, we get (1+x)^2nx^n ...(i) T_r+1= ^2nC_rx^r n ..(ii)Hence coefficient of x^ 1 = ^2nC_ ...

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Binomial Coefficients

Coefficient o...

Question

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

\frac{2 n!}{n - 1! n + 1!}

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\frac{n!}{n - 1! n + 1!}

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\frac{2 n!}{2 n - 1! 2 n + 1!}

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\frac{n!}{2 n - 1! 2 n + 1!}

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Solution

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Similar questions

\frac{1}{x}

(1 + x)^{n} {(1 + \frac{1}{x})}^{n}

\frac{1}{x}

{(1 + x)}^{n} {(1 + \frac{1}{x})}^{n}

\frac{n!}{[(n - 1)! (n + 1)!]}

\frac{(2 n)!}{[(n - 1)! (n + 1)!]}

\frac{(2 n)!}{(2 n - 1)! (2 n + 1)!}

The (n+1)th term from the end in the expansion of $(2 x - \frac{1}{x})^{3 n}$ is:

1 - 2 n + \frac{2 n (2 n - 1)}{2!} - \frac{2 n (2 n - 1) (2 n - 1)}{3!} + . . . + (- 1)^{n - 1} \frac{2 n (n - 1) . . . (n + 2)}{(n - 1)}

= (- 1)^{n + 1} \frac{(2 n)}{2 (n!)^{2}},

x^{n}

(x +^{n} C_{0}) (x + 3 \cdot^{n} C_{1}) \dots (x + (2 n + 1) \cdot^{n} C_{n})

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