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

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

A

`log 2`

B

`log 3`

C

log 5`

D

0

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The correct Answer is:
B
`underset(x to oo)lim((1)/(n)+(1)/(n+1)+...+(1)/(n+2n))`
`=underset(r=0)overset(2n)sum(1)/(n+r)`
`=(1)/(n) underset(r=0)overset(2n)sum(1)/(1+(r)/(n))`
`=int_(0)^(2)(1)/(1+x)dx`
`=[log(1+x)]_(0)^(2)`
`=log3-log 1=log 3`
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