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Show that ("lim")(nvecoo)(1/(n+1)+1/(n+2...

Show that `("lim")_(nvecoo)(1/(n+1)+1/(n+2)++1/(6n))=log6`

A

log 2

B

log3

C

log5

D

log 2

Text Solution

Verified by Experts

The correct Answer is:
D
Let, `l=underset(nrarroo)((1)/(n+1)+(1)/(n+2)+…+(1)/(6n))`
`=underset(nrarroo)(lim)((1)/(n+1)+(1)/(n+2)+…+(1)/(n+5n))`
`l=underset(nrarroo)(lim)sum_(r=1)^(5n)((1)/(n+r))=underset(nrarroo)(lim)(1)/(n)sum_(r=1)^(5n)((1)/(1+(r)/(n)))" ...(i)"`
`because" Lower limit of r = 1"`
`therefore" Lower limit of integration "=underset(nrarroo)(lim)(1)/(n)=0`
`because" Upper limit of r = 5n"`
`therefore" Upper limit of integration "=underset(nrarroo)(lim)(5n)/(n)=5`
From Eq. (i).
`l=int_(0)^(5)(1)/(1+x)dx=[log(1+x)]_(0)^(5)=log6-log1=log6`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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