Sum[Binomial[n, k] x^k/k!, {k, 0, n}]
(* Hypergeometric1F1[-n, 1, -x] *)

Plot[Hypergeometric1F1[-n, 1, -x] /. {x -> 101/100}, {n, 10, 1000},
 AxesLabel -> {"n", "Hypergeometric1F1[-n,1,-x]"}]

Plot[Hypergeometric1F1[-n, 1, -x] /. {x -> -101/100}, {n, 10, 1000},
 AxesLabel -> {"n", "Hypergeometric1F1[-n,1,-x]"}]

Limit[Hypergeometric1F1[-n, 1, -x] /. {x -> 101/100}, n -> Infinity]
(* Infinity *)

Limit[Hypergeometric1F1[-n, 1, -x] /. {x -> -101/100}, n -> Infinity]
(* 0 *)