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Question

Sum to infinite terms of the series cot1(12+34)+cot1(22+34)+cot1(32+34)+....... is

A
π4
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B
tan12
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C
tan13
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D
cot13
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Solution

The correct option is B tan12
Tn=cot1(n2+34)=tan1(1n2+34)=tan1(n+12)tan1(n12)
Sn=nn=1tn=tan1(n+12)tan112S=π2tan112=cot112=Tan12

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