First slide

Binomial theorem for negative integral and rational Index

Question

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

Easy

A

n
B

n - 1
C

n + 2
D

n + 1

Solution

$\begin{matrix} {(1 + x + x^{2} + \dots)}^{2} = {((1 - x)^{- 1})}^{2} = (1 - x)^{- 2} \\ = 1 + 2 x + 3 x^{2} + \dots \end{matrix}$
Therefore, coefficient of xⁿ is n + 1.

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