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underset(n to oo)lim((1)/(n)+(1)/(n+1)+....

`underset(n to oo)lim((1)/(n)+(1)/(n+1)+...+(1)/(3n))` is equal to

A

log 2

B

log3

C

log5

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
`lim_(ntoinfty)((1)/(n)+(1)/(n+1)+...+(1)/(n+2n))`
`=sum_(r=0)^(2n)(1)/(n+r)=(1)/(n)sum_(r=0)^(2n)(1)/(1+(r)/(n))`
`=int_(0)^(2)(1)/(1+x)dx=[log(1+x)]_(0)^(2)-log3-log1=log3`
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