  Treating divergent series properly has been an ongoing issue in mathematics.
However, many of the problems in divergent series stem from the fact that
divergent series were discovered prior to having a number system which could
handle them. The infinities that resulted from divergent series led to
contradictions within the real number system, but these contradictions are
largely alleviated with the hyperreal number system. Hyperreal numbers provide
a framework for dealing with divergent series in a more comprehensive and
tractable way.
