>>111533071/2+1/4+1/8+...+1/2^n = 1-1/2^n
IIRC in the surreal numbers, at n=omega you get 1-1/2^omega, which is infinitesimally close to 1 but not exactly 1. However, if you take n=infinity where infinity is the supremum of all surreals (i.e. the analogue of ordinary calculus' "infinity" but in the surreal numbers, see also order completion) you do get exactly 1.
