Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 5 } \left( n ^ { 2 } - n \right)$
A)40
B)330
C)225
D)15
E)55

Question

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 5 } \left( n ^ { 2 } - n \right)$  
A)40
B)330
C)225
D)15
E)55

Quizplus · Accepted Answer

The sum can be split into two separate sums: $\sum_{n=1}^{5} n^2 - \sum_{n=1}^{5} n$. Using formulas, $\sum_{n=1}^{5} n^2 = \frac{5(5+1)(2*5+1)}{6} = 55$ and $\sum_{n=1}^{5} n = \frac{5(5+1)}{2} = 15$. Therefore, the result is $55 - 15 = 40$.

Find the Sum Using the Formulas for the Sums of Powers