Find the sum to terms of the series .

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Find the sum to nn terms of the series csc⁡−110+csc⁡−150+csc⁡−1170+⋯+csc⁡−1(n2+1)(n2+2n+2)\csc^{-1}\sqrt{10}+\csc^{-1}\sqrt{50}+\csc^{-1}\sqrt{170}+\cdots+\csc^{-1}\sqrt{(n^2+1)(n^2+2n+2)}.

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