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Question

Find the sum to n terms of the series whose nth term is given by

n2+2n

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Solution

Let an be the nth term and 'Sn' be the sum of the n terms of the given series.

an=n2+2n [Given]

Sn=nk=1ak=nk=1(k2+2k)

=(12+21)+(22+22)+(32+23)++(n2+2n)

=(12+22+32++n2)+(21+22+23++2n)

=n(n+1)(2n+1)6+2(2n1)21

=n(n+1)(2n+1)6+2(2n1).


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