To find the sum of a series whose general term is a product of linear factors in ( n ), express the ( n^{th} ) term ( u_n ) as a polynomial in ( n ) and then use the standard summation formulae:
[ \sum_{k=1}^{n} k = \frac{n(n+1)}{2}, \quad \sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}, \quad \sum_{k=1}^{n} k^3 = \left( \frac{n(n+1)}{2} \right)^2 ]
For series of the form ( \sum r \cdot ) (sum of an A.P.), the inner sum can be evaluated first and then the outer sum.