If n∈N, then the coefficient of xn in the expansion of 1-2x+3x2-4x3+....-n is

1-2x+3x2-4x3+....-n=1-x-2-n=1-x2nthen the coefficient of xn is 2nCn

If n∈N, then the coefficient of xn in the expansion of 1-2x+3x2-4x3+....-n is

1-2x+3x2-4x3+....-n=1-x-2-n=1-x2nthen the coefficient of xn is 2nCn

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If $n \in N,$ then the coefficient of xⁿ in the expansion of
${(1 - 2 x + 3 x^{2} - 4 x^{3} + . . . .)}^{- n}$ is

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$n! {2 n_{C}}_{n}$

${2 n_{C}}_{n}$

${2 n_{C}}_{2}$

$\frac{2 n!}{n!}$

answer is C.

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Detailed Solution

${(1 - 2 x + 3 x^{2} - 4 x^{3} + . . . .)}^{- n} = {({(1 - x)}^{- 2})}^{- n}$

$= {(1 - x)}^{2 n}$

then the coefficient of xⁿ is ${2 n_{C}}_{n}$

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If n∈N, then the coefficient of xn in the expansion of 1-2x+3x2-4x3+....-n is

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If $n \in N,$ then the coefficient of xⁿ in the expansion of
${(1 - 2 x + 3 x^{2} - 4 x^{3} + . . . .)}^{- n}$ is