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If the sum of n terms of the series Sn=c...

If the sum of n terms of the series `S_n=cosec^-1sqrt10+cosec^-1sqrt50+cosec^-1sqrt170+...........+cosec^-1sqrt((n^2+1)(n^2+2n+2).` The value of `[lim_(x->oo)s_n]` is

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The correct Answer is:
`tan^(-1) ( n+1) - pi/4 `
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