Converging Power Series, especially the Taylor Series, are used to compute logs, trig functions, roots, etc.. For example:
sin(x) = x - x3/3! + x5/5! - ...
The power series expansion on the right can be directly coded and executed in software to an arbitrary number of terms until the desired precision is attained. So when you hit "sin x" on a calculator, the calculator's software executes the power series.
