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Question Number 106432 by Dwaipayan Shikari last updated on 05/Aug/20

Commented by Dwaipayan Shikari last updated on 05/Aug/20

https://drive.google.com/file/d/12J4x021yiK1X38OHkXoomTz_VuBlcIEt/view?usp=drivesdk

Commented by Dwaipayan Shikari last updated on 05/Aug/20

$$Respectedsirs,kindlygiveatrytothisquestion:)$$

Commented by Dwaipayan Shikari last updated on 05/Aug/20

$$\sqrt{\frac{2}{3}}=\frac{1}{\sqrt{\frac{3}{2}}}=\frac{1}{{(1+\frac{1}{2})}^{\frac{1}{2}}}={(1+\frac{1}{2})}^{-\frac{1}{2}}$$$${(1+\frac{1}{2})}^{-\frac{1}{2}}=1-\frac{1}{2}.\frac{1}{2}+\frac{1.3}{2.4}.{\left(\frac{1}{2}\right)}^2-\frac{1.3.5}{2.4.6}.{\left(\frac{1}{2}\right)}^3+\frac{1.3.5.7}{2.4.6.8}.{\left(\frac{1}{2}\right)}^4-.....$$

Commented by PRITHWISH SEN 2 last updated on 05/Aug/20

$${(1+\mathrm{x})}^{-\frac{1}{2}}=1-\frac{1}{2}\mathrm{x}+\frac{1.3}{2.4}{\mathrm{x}}^2-\frac{1.3.5}{2.4.6}{\mathrm{x}}^3+....$$$$\mathrm{put}\mathrm{x}=\frac{1}{2}\mathrm{you}\mathrm{will}\mathrm{get}\mathrm{the}\mathrm{result}.$$

Commented by PRITHWISH SEN 2 last updated on 05/Aug/20

$$\mathrm{evaluate}$$$$1+\frac{1}{2}-\frac{1.1}{2.4}+\frac{1.1.3}{2.4.6}-\frac{1.1.3.5}{2.4.6.8}+...$$

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