Calculate $S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}$. I know I posted this question already but I want a more detailed answer. For example, how you got from one step to another using the partial fraction formula. Thanks!
2026-03-28 17:25:42.1774718742
Calculate $S =\sum_{k=1}^n\frac {1}{k(k+1)(k+2)}$.
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$\frac {1}{k(k+1)(k+2)} = \left( \frac {1}{k} - \frac {1}{k+1}\right) \frac {1}{k+2} = \frac {1}{k(k+2)} - \frac {1}{(k+1)(k+2)} = \frac{1}{2}\left( \frac {1}{k} - \frac {1}{k+2} \right) - \left( \frac {1}{k+1} - \frac {1}{k+2} \right)$