Find the sum using the formulas for the sums of powers of integers. $$\sum _ { n = 1 } ^ { 22 } \left( n ^ { 3 } - n \right)$$
A)22,770
B)3,795
C)63,756
D)256,036
E)64,009

Question

Find the sum using the formulas for the sums of powers of integers.​ $$\sum _ { n = 1 } ^ { 22 } \left( n ^ { 3 } - n \right)$$ ​
A)22,770
B)3,795
C)63,756
D)256,036
E)64,009

Quizplus · Accepted Answer

We can use the formula for the sum of the first n cubes, which is:

1³ + 2³ + 3³ + ... + n³ = [n(n+1)/2]²

Using this formula, we can find the sum:

1³ + 2³ + 3³ + ... + 34³ = [34(34+1)/2]²
= (17*35)²
= 63,756

Therefore, the best choice is C.

Find the Sum Using the Formulas for the Sums of Powers