It is given in the question that the n^th term of the series,

a_n = n (n + 1) (n + 4)

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

=

=

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, the Sum of the series,