Find the sum of the series whose nth term is given by:

(3n2 + 2n)


It is given in the question that the nth term of the series,


an = 3n2 + 2n


Now, we need to find the sum of this series, Sn.






Note:


I. Sum of first n natural numbers, 1 + 2 +3+…n,



II. Sum of squares of first n natural numbers, 12 + 22 + 32+….n2,



III. Sum of cubes of first n natural numbers, 13 + 23 + 33 +…..n3,



IV. Sum of a constant k, N times,



So, for the given series, we need to find,



From the above identities,




=


=


=


Hence, Sum of the series,


1