The Collaborative International Dictionary of English v.0.48:

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]