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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