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Question

The sum of the nterms of the series 121+(12+22)(1+2)+(12+22+32)(1+2+3)+. is


A

(n+1)(n+2)3

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B

n(n+2)3

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C

n(n+1)3

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D

none of these

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Solution

The correct option is B

n(n+2)3


Find the sum of the given series

121+(12+22)(1+2)+(12+22+32)(1+2+3)+.

Therefore, tn=12+22+32+......+n2(1+2+3+....n)

=n(n+1)(2n+1)6n(n+1)2=2n+13

Sum of the series

=r=1n2n+13=23n(n+1)2+n3=n(n+2)3

Hence, the correct option is OptionB.


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