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Question

If S=n=23n2+1(n21)3, then 16S is

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Solution

Given : S=n=23n2+1(n21)3

We know that,
(n21)3=(n1)3(n+1)3(n+1)3(n1)3=6n2+2

Now, S=n=212((n+1)3(n1)3(n+1)3(n1)3)
S=12n=2(1(n1)31(n+1)3)S=12[(113133)+(123143)+(133153)+]S=12(113+123)S=91616S=9

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