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lim(n rarr oo) (1+4+9+16+...+n^(2))/(4n^...

`lim_(n rarr oo) (1+4+9+16+...+n^(2))/(4n^(3)+1)=`_______.

A

`(1)/(12)`

B

`(1)/(24)`

C

`(1)/(8)`

D

`(1)/(16)`

Text Solution

Verified by Experts

The correct Answer is:
A
Write formula for sum of the squares of first n natural numbers, i.e., `(n(n+1)(2n+1))/(6)`
Divide the numerator and the denominator by `n^(3)`. Then substitute `(1)/(n) = 0, "as" n rarr oo, (1)/(n) = 0`.
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