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Question

limxnr=1tan1(2r1r2+r4) is equal to

A
π/4
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B
π/2
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C
3π4
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D
None of these
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Solution

The correct option is B π/2
Given,
limnnr=1tan1(2r1r2+r4)
NOw,
tan1((r2+r)(r2r)1+(r2+r)(r2r))=tan1(r2+r)tan1(r2r)
summing over r=1 to r=n,the terms will get cancel and we get
=>tan1(n2+n)tan1(0)
=>limntan1(n2+n)
=>tan1()
=>π2

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