Sum of series 1 - e + e²/2! - e³/3! + e⁴/4! +

[Abyssnight]

Homework Statement

Given the following: 1 - e + e²/2! - e³/3! + e⁴/4! + ...
Find the sum of series

Homework Equations

The MacLaurin equation for e^x

The Attempt at a Solution

Well I thought that it would look like $$\sum(-1)^n\frac{e^n}{n!}$$
Tried the Ration Test and got no where. So I'm just kind of stumped

 

[sakodo]

Consider the MacLaurin series for e^x.

e^x = 1 + x + x²/2! + x³/3! + x⁴/4! ...

Now, what do you think you need to put into x to get the alternate series in your question?

 

[Abyssnight]

Wow, haha. I must have had a long night to for some reason miss the obvious. x = -e and it works. Thank you haha.