JEE Mains · Maths · STD 11 - 8. sequence and series
The sum, \(\sum\limits_{n=1}^{7} \frac{n(n+1)(2 n+1)}{4}\) is equal to
- A \(521\)
- B \(663\)
- C \(504\)
- D \(429\)
Answer & Solution
Correct Answer
(C) \(504\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{4}\left(\sum_{n=1}^{7} 2 n^{3}+\sum_{n=1}^{7} 3 n^{2}+\sum_{n=1}^{7} n\right)\) \(=\frac{1}{4}\left(2\left(\frac{7 \times 8}{2}\right)^{2}+3\left(\frac{7 \times 8 \times 15}{6}\right)+\frac{7 \times 8}{2}\right)\) \(=504\)
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