Inverse tangent series via telescoping sums

When first learning about infinite series, students typically are shown some examples for which the partial sums can be simplified by taking advantage of telescoping sums. In this paper, we present many examples of such series, all involving the inverse tangent function and most of which involve the Fibonacci and Lucas numbers. Most of the series presented here have appeared in various papers (see the references), but the authors are usually working in an abstract setting which makes it difficult for students to follow the basic ideas. We seek to make these results accessible to a wider audience.