Find the sum using the formulas for the sums of powers of integers.
$$\sum _ { n = 1 } ^ { 9 } n ^ { 3 }$$
A) 1296
B) 4050
C) 729
D) 285
E) 2025

Question

Quizplus · Accepted Answer

We can use the formula for the sum of cubes of integers, which is:
$$\sum _ { n = 1 } ^ { k } n ^ { 3 } = \left( \frac{k(k+1)}{2}\right) ^2$$
Plugging in $k=9$, we get:
$$\sum _ { n = 1 } ^ { 9 } n ^ { 3 } = \left( \frac{9(10)}{2}\right) ^2 = 2025$$
Therefore, the answer is $\boxed{\text{(E) }2025}$.

Find the Sum Using the Formulas for the Sums of Powers