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$\sin^{- 1} (\frac{1}{\sqrt{2}}) + \sin^{- 1} (\frac{\sqrt{2} - 1}{\sqrt{6}}) + ...... + \sin^{- 1} (\frac{\sqrt{n} - \sqrt{n - 1}}{\sqrt{n (n + 1)}}) + .... \infty =$

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Correct option is B

Tn=sin−1n−n−1nn+1=Tan−1n−n−11+nn−1 =Tan−1n−Tan−1n−1∴S∞=Tan−11−Tan−10+{Tan−12−Tan−11}+......+Tan−1∞=Tan−1∞−Tan−10=π2

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sin−112+sin−12−16+......+sin−1n−n−1n(n+1)+....∞=

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$\sin^{- 1} (\frac{1}{\sqrt{2}}) + \sin^{- 1} (\frac{\sqrt{2} - 1}{\sqrt{6}}) + ...... + \sin^{- 1} (\frac{\sqrt{n} - \sqrt{n - 1}}{\sqrt{n (n + 1)}}) + .... \infty =$