Pensieve header: Runge-Kutta - Taylor comparison.

{(∑_(k=0)^1000)((((-100.))^k)/(k!)), ((((-100.))^1000)/(1000!))}

(∑_(k=0)^1000)N[((((-100))^k)/(k!)),1000]

h=0.1; yj=1.;
Do[
k1=-yj; k2=-(yj+h k1/2); k3=-(yj+h k2/2); k4=-(yj+h k3);
yj=yj+h (k1+2k2+2k3+k4)/6,
{1000}
];
yj

(E^(-100.))