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## Homework Statement

Use partial fractions to show

[tex] \displaystyle\sum_{n=1}^\infty \frac{1}{n(n+1)(n+2)} = \frac{1}{4}[/tex]

## The Attempt at a Solution

I did the partial fraction decomposition to get: [tex] \displaystyle\sum_{n=1}^\infty \frac{1}{2n} - \frac{1}{n + 1} + \frac{1}{2n + 4} [/tex]

I'm not sure how to proceed from here, in my textbook the example shows how terms in the partials sums overlap and cancel out if you start looking at the terms in the partial fraction decomposition, however I can't see that happening with this particular series.

Any suggestions would be appreciated. Thanks in advance.