Find the sum using the formulas for the sums of powers of integers. $$\sum _ { n = 1 } ^ { 6 } n ^ { 2 }$$
A)21
B)42
C)546
D)441
E)91

Name: Find the sum using the formulas for the sums of powers of integers. \[\sum _ { n = 1 } ^ { 6 } n ^ { 2 }\] A)21 B)42 C)546 D)441 E)91
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Question

Find the sum using the formulas for the sums of powers of integers.​ $$\sum _ { n = 1 } ^ { 6 } n ^ { 2 }$$ ​
A)21
B)42
C)546
D)441
E)91

Quizplus · Accepted Answer

The formula for the sum of the squares of the first n natural numbers is $\frac{n(n + 1)(2n + 1)}{6}$. Substituting $n = 6$, we get $\frac{6(6 + 1)(2(6) + 1)}{6} = \frac{6 \cdot 7 \cdot 13}{6} = 7 \cdot 13 = 91$.

Find the Sum Using the Formulas for the Sums of Powers