(* Compute e(x) using Taylor series *)
(* To execute, type << Exp.math at the Mathematica prompt *)

 (* Start with z=1, LIM=5. Seems to work OK. Try z=20 now. *)
 (* You will have to increase LIM to 40 to get reasonable accuracy *)
 (* Now try z = -20  The result is nowhere near the correct value! *)
 (* Moreover, increasing the number of iterations to, say, LIM=41 *)
 (* leads to a very different and again completely wrong answer *)
 (* This is an example of a "bad algorithm". A "good algorithm" will *)
 (* compute e^-20 as e^-20 = 1/e^20  *)
  

z= 1.0 
LIM = 5 

Print["Taylor series result for e(z):"]

Print [NSum[z^k/k!, {k, 0, LIM}] ]

Print["Exact result:"]

Print [ Exp[z] ]

Clear[z]
Clear[LIM]