Poisson distribution sum for even integers

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Firstly can anyone tell me if the steps that I've done so far are correct or not. Then, I have a series going up to infinity and I'm not able to understand how to sum this series.

I was not aware that this is the hyperbolic cosine series but having just looked at that series, I think the sum of this Poisson series would be the sum from 0 to infinity of ((0.24)^2n)/2n!, but how do I get a value for this infinite series sum?

Got it!

Any help would be much appreciated.