I am trying to calculate the following sum:
$$\sum_{i=0}^\infty \dfrac{e^{-\lambda}\lambda^{2i}}{(2i)!}, 0 \lt\lambda \lt 1$$
It is clearly a power series, however I am stuck trying to move beyond this conclusion. I tried to solve it using wolfram alpha and it gives the following answer: $e^{-\lambda} \cosh(\lambda)$. What would be the approach to get the answer the wolfram alpha gives me?
Thanks!