Editing Series (mathematics) (section)

=== Asymptotic series ===
{{Main|Asymptotic expansion}}
[[Asymptotic series]], typically called [[asymptotic expansion]]s, are infinite series whose terms are functions of a sequence of different [[Big O notation|asymptotic orders]] and whose partial sums are approximations of some other function in an [[asymptotic limit]]. In general they do not converge, but they are still useful as sequences of approximations, each of which provides a value close to the desired answer for a finite number of terms. They are crucial tools in [[perturbation theory]] and in the [[analysis of algorithms]].

An asymptotic series cannot necessarily be made to produce an answer as exactly as desired away from the asymptotic limit, the way that an ordinary convergent series of functions can. In fact, a typical asymptotic series reaches its best practical approximation away from the asymptotic limit after a finite number of terms; if more terms are included, the series will produce less accurate approximations.