diverging series
Webster's Dictionary (GCIDE)
Diverging \Di*ver"ging\, a. Tending in different directions from a common center; spreading apart; divergent. [1913 Webster]
Diverging series (Math.), a series whose terms are larger as the series is extended; a series the sum of whose terms does not approach a finite limit when the series is extended indefinitely; -- opposed to a converging series. [1913 Webster]