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  • <img alt="\small 1-\frac{1}{8}+\frac{1}{8} \cdot \frac{3}{16}-\frac{1.3 .5}{8.16 .24}+\ldots . ." src="https://entrancecorner.oncodecogs.com/gif.latex?%5Csmall%201-%5Cfrac%7B1%7D%7B8%7D&plus;%5

\small 1-\frac{1}{8}+\frac{1}{8} \cdot \frac{3}{16}-\frac{1.3 .5}{8.16 .24}+\ldots . .

 

Option: 1

\frac{2}{5}


Option: 2

\frac{\sqrt{2}}{5}


Option: 3

\frac{2}{\sqrt{5}}


Option: 4

None of these
 


Answers (1)

best_answer

Comparing the given expression to

\begin{aligned} & 1+n x+\frac{n(n-1)}{2 !} x^2+\ldots i . e .(1+x)^n \text {, we get } \\ & n x=-\frac{1}{8} \text { and } \frac{n(n-1)}{2 !} x^2=\frac{3}{128} \Rightarrow x=\frac{1}{4}, n=-\frac{1}{2} \end{aligned}

\\Hence \\ 1-\frac{1}{8}+\frac{1}{8} \cdot \frac{3}{16}-\ldots=\left(1+\frac{1}{4}\right)^{-1 / 2}=\frac{2}{\sqrt{5}}

Posted by

Ritika Kankaria

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