Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 2 } n ^ { 4 }$
A)33
B)17
C)30
D)5
E)9

Name: Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 2 } n ^ { 4 }$ A)33 B)17 C)30 D)5 E)9
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Question

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 2 } n ^ { 4 }$  
A)33
B)17
C)30
D)5
E)9

Quizplus · Accepted Answer

The sum of the fourth powers of the first n integers is given by the formula $\sum_{n=1}^{k} n^4 = \frac{k(k+1)(2k+1)(3k^2+3k-1)}{30}$. For $k=2$, this evaluates to $\frac{2(3)(5)(17)}{30} = 17$.

Find the Sum Using the Formulas for the Sums of Powers