In this article we demonstrate how the Laplace transform can be used as a tool to find closed form expressions for certain infinite series. Sometimes the summand of a series can be realized as a Laplace transform integral. If this is the case, and if the order of summation and integration can be interchanged (with justification of course), then the series can be written as an integral; if this integral can be evaluated, then we have a closed form expression for the series. The purpose of this article is to explain this technique, and to illustrate with several examples.