Here is an algorithm for approximating an infinite series by using a partial sum plus an error corrector derived from the Integral Test. This gives much more powerful error control than merely using partial sums to approximate the series. This technique can be used to quickly approximate some series that Maple cannot already approximate, and thus the power of Maple is extended significantly. Audience:
1. Calculus students learning about the integral test who are interested in some of the finer computational aspects. 2. Numerical analysis students learning how to approximate series. 3. Computational professionals interested in learning efficient Maple techniques.