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Question

Sum of first n terms in the following series

cot13 + cot17 + cot113 + cot121 + .........n terms.is given by


A

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B

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C

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D

All of these

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Solution

The correct option is D

All of these


Let S = 3 + 7 + 13 + 21 + ...... + TπTπ = n2 + n + 1.

Let Tr = cot1( r2 + r + 1) = tan1(r + 1) - tan1r.

Put r = 1, 2,........, n and add, we get the required sum

tan1(n+1) - tan11 = tan1( nn+2) =cot1 (n+2n)


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