A) \[\frac{2}{5}\]
B) \[\frac{\sqrt{2}}{5}\]
C) \[\frac{2}{\sqrt{5}}\]
D) None of these
Correct Answer: C
Solution :
Comparing the given expression to \[1+nx+\frac{n(n-1)}{2!}{{x}^{2}}+....i.e.{{(1+x)}^{n}},\]we get \[nx=-\frac{1}{8}\]and \[\frac{n(n-1)}{2!}{{x}^{2}}=\frac{3}{128}\Rightarrow x=\frac{1}{4},n=-\frac{1}{2}\] Hence \[1-\frac{1}{8}+\frac{1}{8}.\frac{3}{16}-....={{\left( 1+\frac{1}{4} \right)}^{-1/2}}=\frac{2}{\sqrt{5}}\]
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