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Question

The sum of the series 312+512+22+712+22+32+.... upto n terms, is

A
nn+1
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B
n+2n+1
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C
6nn+1
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D
6(n+2)n+1
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Solution

The correct option is C 6nn+1
The nth term in the given series can be written as,
tn=2n+112+22+.....+n2

or, tn=2n+1n(n+1)(2n+1)6

or, tn=6n(n+1)

or, tn=6(n+1)+6n.

The sum of the series upto n terms will be,

k=nk=1tk

=k=nk=1(6k6k+1)

=6162+6263+63..........6n+6n6n+1.

=66n+1

=6nn+1.

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