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

The value of `underset(ntooo)lim[(1)/(n)+(e^(1//n))/(n)+(e^(2//n))/(n)+...+(e^((n-1)//n))/(n)]` is

A

e

B

`-e`

C

`e-1`

D

`1-e`

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`lim_(xto oo) (1)/(n){1+e^(1//n)+e^(2//n)+.....+e^((n-1)/(n))}`
` =lim_(xto oo) (1)/(n){(1-(e^(1//n))^n)/(1-e^(1//n))}=lim_(xto oo) (1-e)/(((1-e^(1//n))/(1//n)))=(1-e)/(-1)=e-1`.
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