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Question

Value of the following expression is limn1n3(12+22+32++n2)

A
13
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B
16
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C
12
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D
23
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Solution

The correct option is A 13
We know that,
(12+22+32+...+n2)=n(n+1)(2n+1)6
limn1n3(12+22+32++n2) =limnn(n+1)(2n+1)6n3
=limn(1+1n)(2+1n)6 =1×26=13

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