How do you find the sum of factorials #1! + 2! + 3!+ ................... + n!?#?

1 Answer
Konstantinos Michailidis
May 23, 2016

The formula below computes this sum

#\sum_{k = 0}^{n} k! = \frac{i\pi}{e} + \frac{\text{Ei}(1)}{e} - \frac{(-1)^n\ \Gamma[n+2]\ \Gamma[-n-1, -1]}{e}#

Where #Ei# is the Exponential Integral function, and #Γ[x]# is the Euler Gamma Function whilst #Γ[x,n]# is the upper incomplete Gamma Function.

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