Evaluating Infinite Series: (2^n)/(n!) from n=0 to infinity

[lvuittongirl22]

How do I evaluate the infinite series (2^n)/(n!) from n=0 to infinity?
(I don't know how you put the little E symbol and all that in so I had to write it out.)

I already found that it converges to 0 using the ratio test, but I don't know quite how to evaluate it.

Any help would be mondo appreciated! Thank you!

 

[HallsofIvy]

Have you dealt with Taylor's series? In particular, do you know the Taylor's series for e^x?

 

[lvuittongirl22]

We went over them, but I'm not sure how to use them...