Coefficient of $x^{r}$ in the expansion of $(1 - 2 x)^{- 1 / 2}$ is

\frac{(2 r)!}{(r!)^{2}}

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\frac{(2 r)!}{2^{r} (r!)^{2}}

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\frac{(2 r)!}{(r!) 2^{2 r}}

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\frac{(2 r)!}{2^{r} (r + 1)! (r + 1)}

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Solution

The correct option is A $\frac{(2 r)!}{(r!)^{2}}$
Coefficient of $x^{r}$ in the expansion of
${(1 - 2 x)}^{- \frac{1}{2}}$
by using binomial expansion
$\begin{matrix} \Rightarrow \frac{[\frac{1}{2} (\frac{1}{2} + 1) (\frac{1}{2} + 2) . . . . . . . . . . . (\frac{1}{2} + r - 1) (2 x)]}{(r!)} \Rightarrow \frac{\frac{1}{2} . \frac{3}{2} . \frac{5}{2} . . . . . . . . . (r - \frac{1}{2}) 2^{r} x^{r}}{(r!)} = \frac{2 r!}{{(r!)}^{2}} \end{matrix}$

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