Calculating the Sum of Infinite Series: 2^k/k! Method

[apiwowar]

how would i go about finding the sum of the infinite series 2^k/k!?

its not a geometric so i can't use the formulas for that so i really have no clue.

any help would be appreciated

 

[Dick]

It might help to know the taylor expansion of e^x.

 

[apiwowar]

i was thinking that but could that work since that's not a power series?

 

[Dick]

i was thinking that but could that work since that's not a power series?

The taylor expansion of e^x IS a power series. It's not geometric, I'm not sure what you are worried about.

 

[apiwowar]

wait nevermind, i was confusing myself.
so what I am talking about would be the closed form for the taylor series e^2 then, right?

 

[Dick]

wait nevermind, i was confusing myself.
so what I am talking about would be the closed form for the taylor series e^2 then, right?

I don't see anything wrong with that.

 

[apiwowar]

thanks