Two important techniques in the ad hoc evaluation of series are telescoping and partial fraction decomposition. The latter is useful in calculus too, as an integration technique for rational functions. We show an example here of an infinite series $$\frac{1}{1\cdot 2 \cdot 3}+\frac{1}{2\cdot 3\cdot 4}+\cdots$$ that uses both telescoping and partial fraction decomposition in its evaluation.
