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What is lim(ntooo) (1+2+3+......+n)/(1^(...

What is `lim_(ntooo) (1+2+3+......+n)/(1^(2)+2^(2)+3^(2)+......n^(2))`

A

5

B

2

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
`underset(ntooo)lim(1+2+3+......+n)/(1^(2)+2^(2)+3^(3)+......+n^(2))=underset(ntooo)lim(n(n+1))/(2/((n(n+1)(2n+1))/(6)))`
`:.underset(ntooo)lim(3)/(2n+1)=0`
Note : `1+2+3+......+n=(n(n+1))/(2)`
`1^(2)+2^(2)+3^(3)+......+n^(2)=(n(n+1)(2n+1))/(6)`
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