If n is a positive integer,then the coefficie | vedclass

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(C) We know that the series expansion of $(1+x)^{-2}$ is given by:$(1+x)^{-2} = 1 - 2x + 3x^2 - 4x^3 + \ldots$Therefore,the given expression can be wr

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$^{(2n)}C_6$

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(C) We know that the series expansion of $(1+x)^{-2}$ is given by:$(1+x)^{-2} = 1 - 2x + 3x^2 - 4x^3 + \ldots$Therefore,the given expression can be written as:$(1-2x+3x^2-4x^3+\ldots)^{-n} = [(1+x)^{-2}]^{-n} = (1+x)^{2n}$Now,using the Binomial Theorem,the general term in the expansion of $(1+x)^{2n}$ is given by:$T_{r+1} = ^{(2n)}C_r x^r$To find the coefficient of $x^6$,we set $r = 6$:$T_{6+1} = ^{(2n)}C_6 x^6$Thus,the coefficient of $x^6$ is $^{(2n)}C_6$.

If $n$ is a positive integer,then the coefficient of $x^6$ in the expansion of $(1-2x+3x^2-4x^3+\ldots)^{-n}$ is

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