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Question

The value of limn[n1+n2+n4+n2+n9+n2++12n] is equal to [Bihar CEE 1994]


A

π2

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B

π4

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C
1
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D

None of these

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Solution

The correct option is B

π4


We have, limn[n1+n2+n4+n2++12n]
=limnnr=1nr2+n2=limnnr=1nn2(1+r2n2)
=limnnr=11n⎜ ⎜11+r2n2⎟ ⎟=10dx1+x2,
{Applying formula, limnn1r=1{f(rn)}1n=10f(x)dx}
=[tan1x]10=tan11tan10=π4


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