In the expansion of 1 - x-1 - x2- the coefficient of xn

The correct option is B Given term can be written as (1 + x)^2(1 x)^ 2 =(1 + 2x + x^2)[1 + 2x + 3x^2 + .......+(n 1)x^n 2+nx^n 1+(n+1)x^n+...........] = x ...

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Byju's Answer

Standard XI

Mathematics

Binomial Coefficients

In the expans...

Question

In the expansion of $(\frac{1 + x}{1 - x})^{2}$ , the coefficient of $x^{n}$

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Solution

The correct option is A

Given term can be written as $(1 + x)^{2}$ $(1 - x)^{- 2}$

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

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

Therefore coefficient of $x^{n}$ is 4n.

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In the expansion of (1+x1−x)2, the coefficient of xn

The correct option is A Given term can be written as (1+x)2(1−x)−2 =(1+2x+x2)[1+2x+3x2+.......+(n−1)xn−2+nxn−1+(n+1)xn+...........] = xn(n+1+2n+n−1)+.......... Therefore coefficient of xn is 4n.

In the expansion of $(\frac{1 + x}{1 - x})^{2}$ , the coefficient of $x^{n}$