The sum, _ n=1 ^ 7 n(n+1)(2 n+1) 4 is equal to - Vidyadip

Question

The sum, $\sum\limits_{n=1}^{7} \frac{n(n+1)(2 n+1)}{4}$ is equal to

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Answer

c
$\frac{1}{4}\left(\sum_{n=1}^{7} 2 n^{3}+\sum_{n=1}^{7} 3 n^{2}+\sum_{n=1}^{7} n\right)$

$=\frac{1}{4}\left(2\left(\frac{7 \times 8}{2}\right)^{2}+3\left(\frac{7 \times 8 \times 15}{6}\right)+\frac{7 \times 8}{2}\right)$

$=504$

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