A good trigonometry FIITJEE problem!

Geometry Level 3

π ÷ ∑ n = 1 ∞ sin ⁡ − 1 [ n − n − 1 n ( n + 1 ) ] = ? \large\pi \div \sum_{n=1}^{\infty}\sin^{-1}\left[\dfrac{\sqrt{n}-\sqrt{n-1}}{\sqrt{n(n+1)}}\right] = \ ?


The answer is 2.

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Adarsh Kumar by Adarsh Kumar , 21, India

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1 solution

arcs in(√n-√(n-1))/√{n(n+1) =arcsin[{√(1/n) √(n/(n+1))-√((n-1)/n) 1/√(n+1) Now take1/√n as sina and 1/√(n+1)as sinb. Now it will continue as a telescopic series. First we get arcs in(1) and last we getarcsin(0). Then its solved.

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