# Identify The Series!

Calculus Level 5

$\dfrac { n! }{ { a }_{ n-1 } } ={ a }_{ n }$

Consider a recurrence relation above for $$n = 1,2,3,\ldots$$ and $$a_0 = 1$$. If the value of the series $$\displaystyle \sum_{n=0}^\infty \dfrac1{a_{2n} }$$ can be expressed as $$e^{\alpha /\beta}$$, where $$\alpha$$ and $$\beta$$ are coprime positive integers, find $$\alpha+\beta$$.

Clarification: $$e \approx 2.71828$$ denotes the Euler's number.

×