First slide

Binomial theorem for negative integral and rational Index

Question

The coefficient of x⁵ in ${(1 + 2 x + 3 x^{2} + \dots)}^{- 3 / 2}$ is $(| x | < 1)$

Easy

A

21
B

25
C

26
D

0

Solution

$\begin{matrix} {(1 + 2 x + 3 x^{2} + \dots)}^{- 3 / 2} = {[(1 - x)^{- 2}]}^{- 3 / 2} \\ = (1 - x)^{3} = 1 - 3 x + 3 x^{2} - x^{3} \end{matrix}$
Therefore, coefficient of x⁵ is 0.

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