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The value of lim(ntooo)[n/(n^(2)+1^(2)...

The value of
`lim_(ntooo)[n/(n^(2)+1^(2))+n/(n^(2)+2^(2))+………….+n/(n^(2)+n^(2))]`, is

A

`(pi)/4`

B

`log2`

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`lim_(nto oo) `
`[n/(n^(2)+1^(2))+n/(n^(2)+2^(2))+..+n/(n^(2)+n^(2))]`
`lim_(nto oo) 1/nsum_(r=1)^(n)1/(1+(r/n)^(2))`
`=int_(0)^(1)(dx)/(1+x^(2))[tan^(-1)x]_(0)^(1)=(pi)/4`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 13-PAPER II OBJECTIVE TYPE
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