The coefficient of x^n in the expansion of (1 | vedclass

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(B) We know that the series expansion of $(1+x)^{-2}$ is $1 - 2x + 3x^2 - 4x^3 + \dots$ for $|x| < 1$.Substituting this into the given expression,we g

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$\frac{(2n)!}{(n!)^2}$

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(B) We know that the series expansion of $(1+x)^{-2}$ is $1 - 2x + 3x^2 - 4x^3 + \dots$ for $|x| Substituting this into the given expression,we get:$(1 - 2x + 3x^2 - 4x^3 + \dots)^{-n} = [(1+x)^{-2}]^{-n} = (1+x)^{2n}$.Now,we need to find the coefficient of $x^n$ in the expansion of $(1+x)^{2n}$.Using the Binomial Theorem,the general term in the expansion of $(1+x)^{2n}$ is given by $\binom{2n}{r} x^r$.For $r = n$,the coefficient is $\binom{2n}{n} = \frac{(2n)!}{n!(2n-n)!} = \frac{(2n)!}{(n!)^2}$.

The coefficient of $x^n$ in the expansion of $(1 - 2x + 3x^2 - 4x^3 + \dots)^{-n}$ is

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