We present a definition for the sum of a sequence of combinatorial games. This sum coincides with the classical sum in the case of a converging sequence of real numbers and with the infinitary natural sum in the case of a sequence of ordinal numbers. We briefly discuss other possibilities, such as the string limit, some "magical" variants of Hackenbush, as well as "Dadaist" infinite sums, which allow transfinite runs, while still being loopfree.