# Proving that the sum of (u^x)/x! from 0 to infinity = e^u

1. Apr 21, 2013

### CraigH

2. Apr 21, 2013

### tiny-tim

Hi CraigH!

Isn't that the definition of eu ?

(and you can check it by working out euev, or by differentiating it )

3. Apr 21, 2013

### dextercioby

Do you know about the MacLaurin series expansion ? What is it for ex ?

4. Apr 21, 2013

### CraigH

Ah yes, I've just looked up the MacLaurin series for e^x in my data book, its give me the answer i was hoping for. I needed to know as part of a proof for a different equation.

So in my exam just saying:

"From the MacLaurin series:
The sum of (u^x)/x! from 0 to infinity = e^u"

Should be enough then.