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If $| x | < 1$ , then the coefficient of $x^{n}$ in expansion of ${(1 + x + x^{2} + x^{3} + \dots)}^{2}$ is

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$n - 1$

$n$

$n + 2$

$n + 1$

answer is D.

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Detailed Solution

${(1 + x + x^{2} + x^{3} + \dots)}^{2} = {({(1 - x)}^{- 1})}^{2} = (1 - x)^{- 2}, (1 - x)^{- 2} = 1 + 2 x + 3 x^{2} + 4 x^{3} + . . . . + (r + 1) x^{r} + . . . . . . . coefficient of x^{n} = n + 1$

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