Find the sum using the formulas for the sums of powers of integers. $$\sum _ { n = 1 } ^ { 14 } n ^ { 3 }$$
A)6,090
B)105
C)11,025
D)1,015
E)210

Question

Find the sum using the formulas for the sums of powers of integers.​ $$\sum _ { n = 1 } ^ { 14 } n ^ { 3 }$$ ​
A)6,090
B)105
C)11,025
D)1,015
E)210

Quizplus · Accepted Answer

Using the formula for the sum of the first n squares: 
1^2 + 2^2 + 3^2 + ... + 100^2 = n(n+1)(2n+1)/6
where n = 100, we get:
1^2 + 2^2 + 3^2 + ... + 100^2 = 100(101)(201)/6 = 338,350
Therefore, the answer is C) 11,025.

Find the Sum Using the Formulas for the Sums of Powers