The sum _n=1^7(n(n+1)(2n+1))/(4) is equal to ________.

Question

The sum $\displaystyle\sum_{n=1}^{7}\frac{n(n+1)(2n+1)}{4}$ is equal to \_\_\_\_\_\_\_\_.

Answer: 504

Accepted Answer

$$\frac14\sum_{n=1}^{7}(2n^3+3n^2+n) = \frac14\left[2\left(\frac{7\times8}{2}\right)^2+3\cdot\frac{7\times8\times15}{6}+\frac{7\times8}{2}\right] = \frac{1568+420+28}{4} = 504.$$

Solutions · 1