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lim (n to oo) ( 1/(n^(2)+1^(2)) + 1/(n^(...

` lim _(n to oo) ( 1/(n^(2)+1^(2)) + 1/(n^(2)+2^(2)) +...1/(2n^(2)))` equals

A

`(pi)/(6)`

B

`(pi)/(4)`

C

`(pi)/(3)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `S=(1^(lim))/(n_(nrarroo))((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+...+(n)/(n^(2)+n^(2)))`
`S=(1)/(n)underset(nrarroo)(lim)sum_(r=1)^(n)(1)/(1+((r)/(n))^(2))`
`S=int_(0)^(1)(dx)/(1=x^(2))=[tan^(-1)x]=(pi)/(4)`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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