Find the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot (n+1) \cdot (n+2)}$

Asked Mar 26 '15 at 13:52

Active Jul 29 '15 at 22:56

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I am trying to find the sum of the following series $$\sum_{n=1}^{\infty} \frac{1}{n \cdot (n+1) \cdot (n+2)}$$

I've already figured it out that it converges and, as it looks like a telescoping series, I also tried decomposing it into partial fractions, which would be $$\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2n+4}$$ But that doesn't seem to be helping me at all... Any ideas?

asked Mar 26 '15 at 13:52

Frank

See also: Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$ and What is the proof for $\sum_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)} = \frac{1}{4}$ – Martin Sleziak Jul 30 '15 at 09:11

Find the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n \cdot (n+1) \cdot (n+2)}$

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