Power series are series in an indeterminatex. For some values of x, the power series may converge, for others it may diverge. The range of all those x, for which a power series converges, is the convergence region of the power series. The task for power series is usually to determine the convergence region K for this series. The set K plays an important role: Every power series provides a function on K; in this way we obtain important functions.