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Given that lim(nto oo) sum(r=1)^(n) (l...

Given that
`lim_(nto oo) sum_(r=1)^(n) (log (r+n)-log n)/(n)=2(log 2-(1)/(2))`,
` lim_(n to oo) (1)/(n^k)[(n+1)^k(n+2)^k.....(n+n)^k]^(1//n)`, is

A

`(4k)/(e)`

B

`ksqrt((4)/(e)`

C

`((4)/(e))^k`

D

`((e)/(4))^k`.

Text Solution

Verified by Experts

The correct Answer is:
C
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