MCQ
The sum, $\sum\limits_{n=1}^{7} \frac{n(n+1)(2 n+1)}{4}$ is equal to
- A$521$
- B$663$
- ✓$504$
- D$429$
✓
Answer
Correct option: C.
$504$
c
$\frac{1}{4}\left(\sum_{n=1}^{7} 2 n^{3}+\sum_{n=1}^{7} 3 n^{2}+\sum_{n=1}^{7} n\right)$
$\frac{1}{4}\left(\sum_{n=1}^{7} 2 n^{3}+\sum_{n=1}^{7} 3 n^{2}+\sum_{n=1}^{7} n\right)$
$=\frac{1}{4}\left(2\left(\frac{7 \times 8}{2}\right)^{2}+3\left(\frac{7 \times 8 \times 15}{6}\right)+\frac{7 \times 8}{2}\right)$
$=504$
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