# Find the sum of the series 2

Calculus Level 4

$\large 1+\dfrac{1+7}{1!} + \dfrac{1+7+7^2}{2!} + \dfrac{1+7+7^2+7^3}{3!} +\cdots$

If the above sum can be represented in the form of $$\dfrac{ae^a-e}{b}$$, then find the value of $$a+b$$.


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

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