A = 
        1 + (1/2) (s^2) 
            dt + (1/4) ( 
              (r^2) +  (((r + (s^2)))^2)) (dt^2);

d = A - Sqrt[(A^2) - 1];

ds = Series[d, {dt, 0, 2}]

u = A + Sqrt[(A^2) - 1];

us = Series[u, {dt, 0, 2}]

p = (((E^(r dt)) - d)/(u - d));

ps = Series[p, {dt, 0, 2}];

(E^(-r dt)) (ps Vp  +  (1 - ps) Vp)