This paper presents closed-form expressions for pricing Bermudan options in terms of an infinite series of standard solutions of the Black-Scholes equation. These standard solutions are combined for successive exercise dates using backward induction. At each exercise date, the optimal exercise price of the underlying asset is the root of a one-dimensional nonlinear algebraic equation. Numerical examples demonstrate the convergence of the series to the solution obtained using alternative methods. The work presented precedes a more general approach for Bermudan options on multiple assets involving multi-dimensional Hermite polynomials.