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# Explain this sum to infinity please watch

1. Hi I have in my notes this sum to infinity, starting from i=0, can someone explain it to me:

(4^(2i))/((2i)!) = (e^4 + e^(-4))/2

I know that the sum to infinity starting from i = 0

(4^i)/i! is equal to e^-4

so could someone explain the above sum to me please.

Thanks.
2. (Original post by TheBhramaBull)
Hi I have in my notes this sum to infinity, starting from i=0, can someone explain it to me:

(4^(2i))/((2i)!) = (e^4 + e^(-4))/2

I know that the sum to infinity starting from i = 0

(4^i)/i! is equal to e^-4

so could someone explain the above sum to me please.

Thanks.
Think cosine hyperbolic.

edit: Alternatively, sum together the Taylor series expansions for and , and it should be clear that their sum is twice the sum to infinity in question, for an approproiate choice of x.

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