A) \[1-\frac{3}{2}x+\frac{3}{8}{{x}^{2}}-\frac{1}{16}{{x}^{3}}\]
B) \[1-\frac{3}{2}x-\frac{3}{8}{{x}^{2}}-\frac{{{x}^{3}}}{16}\]
C) \[1-\frac{3}{2}x+\frac{3}{8}{{x}^{2}}+\frac{{{x}^{3}}}{16}\]
D) None of these
Correct Answer: C
Solution :
\[{{(1-x)}^{3/2}}\] \[=\left[ 1+\frac{3}{2}(-x)+\frac{3}{2}.\frac{1}{2}.\frac{1}{2!}{{(-x)}^{2}}+\frac{3}{2}.\frac{1}{2}\left( -\frac{1}{2} \right)\frac{1}{3!}{{(-x)}^{3}}+... \right]\] \[=1-\frac{3}{2}x+\frac{3}{8}{{x}^{2}}+\frac{{{x}^{3}}}{16}\](only four terms).
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