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

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

Quizplus · Accepted Answer

The formula for the sum of the cubes of the first n natural numbers is $\frac{n^2(n+1)^2}{4}$. Plugging in $n = 9$, we get $\frac{9^2(10)^2}{4} = \frac{81 \cdot 100}{4} = 2025$.

Find the Sum Using the Formulas for the Sums of Powers