Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 7 } n ^ { 5 }$
A)840
B)29,008
C)4,676
D)784
E)140

Name: Find the sum using the formulas for the sums of powers of integers. $\sum _ { n = 1 } ^ { 7 } n ^ { 5 }$ A)840 B)29,008 C)4,676 D)784 E)140
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Question

Find the sum using the formulas for the sums of powers of integers.   $\sum _ { n = 1 } ^ { 7 } n ^ { 5 }$  
A)840
B)29,008
C)4,676
D)784
E)140

Quizplus · Accepted Answer

The sum of the fifth powers of the first n natural numbers is given by the formula $\frac{n^2(n+1)^2(2n^2+2n-1)}{12}$. Plugging in $n=7$, we get $\frac{7^2(8)^2(2(7)^2+2(7)-1)}{12} = 29,008$.

Find the Sum Using the Formulas for the Sums of Powers