Given that and

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

Given that ∑k=1nk=n(n+1)2\sum_{k=1}^{n}k=\frac{n(n+1)}{2} and ∑k=1nk2=n(n+1)(2n+1)6\sum_{k=1}^{n}k^2=\frac{n(n+1)(2n+1)}{6}, write ∑k=1n(k+1)(k+2)\sum_{k=1}^{n}(k+1)(k+2) in simplest form. Check your answer when n=10n=10. (a) Write ∑k=1n(k+1)(k+2)\sum_{k=1}^{n}(k+1)(k+2) in simplest form. (b) Check the result when n=10n=10.

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