How to prove that exp(x) is not uniform convergent in R?

Hi all,

exp(x)=1+x+x^2/2+x^3/3!+ ...

it is not uniform convergent on the whole R,

How to show that?

Thanks a lot!

.

Follow-Ups:
- Re: How to prove that exp(x) is not uniform convergent in R?
  - From: Peter Allen
- Re: How to prove that exp(x) is not uniform convergent in R?
  - From: Peter L. Montgomery
- Re: How to prove that exp(x) is not uniform convergent in R?
  - From: Julien Santini