For $|x|

Question

For $|x| < 1$, the constant term in the expansion of $\frac{1}{(x - 1)^{2}(x - 2)}$ is

Dr. Abubacker · Accepted Answer

(d)
$\because\frac{1}{(x - 1)^{2}(x - 2)} = \frac{1}{{- 2(1 - x)}^{2}\left( 1 - \frac{x}{2} ight)}$
$= - \frac{1}{2}\left\lbrack (1 - x)^{- 2}\left( 1 - \frac{x}{2} ight)^{- 1} ightbrack$
$= - \frac{1}{2}\left\lbrack (1 + 2x + ...)\left( 1 + \frac{x}{2} + ... ight) ightbrack$
$	herefore$ Coefficient of constant term is $- \frac{1}{2}$

Q. For $|x| < 1$, the constant term in the expansion of $\frac{1}{(x - 1)^{2}(x - 2)}$ is

Explanation

Reviewed by Dr. Abubacker

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