${(1 - x)}^{3 / 2}$ can be expanded in ascending powers of $x$ if

- 1 < x < 1

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x < - 1

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x > 1

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none of these

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Solution

The correct option is A $- 1 < x < 1$
Given, $(1 - x)^{\frac{3}{2}}$
$= (1 - x) [\sqrt{1 - x}]$
Hence this can only be expanded in powers of x if
$| x | < 1$
$\to - 1 < x < 1$

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