Summing Maclaurin Series for x^2

[JakeD]

Homework Statement

How do I find the sum of \sum\frac{x^{2k}}{k!}?

The Attempt at a Solution

I tried transforming various known Taylor series, such as sin x, e^x, and so on, but they didn't fit for 2 reasons:
1. In all of them, the degree of the factor equals the power of x. i.e. if you have x^2k in the nominator, then you have (2k)! in the denominator, whereas here, you have x^2k in the nominator, while having k! (not (2k!)) in the denominator.

2. In sin x, you have alternating pluses and minuses, while in the required sum, they are all pluses.Any help will be appreciated

 

[JakeD]

OK, found the solution.

By replacing x with x^2 in the Taylor series of e^x, I get the desired sum.