A limit of a sequence

Questions
,
1

Hi,

I do not understand the limit given below. As far as I know the terms of sequence belong to the open interval ]0,1[
and the limit equals 1. Please let me know where I am wrong.

Clear[n]
Limit[n n! (E - Sum[1/k!, {k, 0, n}]), n -> ]
  • Marian Muresan
2

Please consider entering the code using the editor-spikey, otherwise it gets tousled. The following code also produces myLim = 1. (Deleted my earlier notes, which did not apply to a sum to infinity).

(* iabraham, Mathematica 7.0.1.0, Win-7-64b *)
Clear["Global`*"];
myLim[lim_] := Limit[n n! (E - SetPrecision[Sum[(1/k!), {k, 0, n}], 10]), n -> lim]
3 
In[26]:= Limit[n n! (E - Sum[1/k!, {k, 0, n}]), n -> Infinity]




Out[26]= 1