# Find the sum of the series

Calculus Level 5

$\large 1+\frac{1^2+2^2}{2!} + \frac{1^2+2^2+3^2}{3!} + \frac{1^2+2^2+3^2+4^2}{4!} + \cdots$

If the value of the sum above can be expressed in the form of $\dfrac{ae}{b}$, where $a$ and $b$ are coprime positive integers, find $a+b$.


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

×