ABSTRACT
We have seen many instances in which we can solve a difficult problem in terms of a series. Sometimes the series is slowly converging, so that it takes many terms of the series to get a decent amount of accuracy to the problem. Furthermore, the terms of the series may not follow a simple pattern, so it takes a major effort just to get a handful of terms. To make matters worse, many of the asymptotic series turned out to be divergent. Although the optimal truncation rule allowed us to get a few places of accuracy from the series, the results were limited. The goal of this section is to milk the most out of what few terms of the series we have to get as much accuracy as possible.
