The coefficient of x^n inthe expansion of (1-2x+3x^2-4x^3+... \to \infty)^{-n} is

NIMCET 2018 Question Paper with solutions

Question : 29 of 120

Marks: +1, -0

The coefficient of

x^n

inthe expansion of

(1-2x+3x^2-4x^3+... \to ∞)^{-n}

Solution:

by Binomial expansion
∴

(1-2x+3x^2-4x^3+... \to ∞)^{-n}

(1+x)^{2n}

Now, rth term in the expansion of

(1+x)^{2n}

↖{2n}C_r(1)^{2n-r}(x)^r

For

x^n

, put r = n
∴ Coefficient of

x^n

↖{2n}C_n

and

↖{2n}C_n

{2n!}/{(2n-n)!n!}

(2n!)/(n!)^2

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