What is the value of the harmonic factorial series sum?

[terryds]

Homework Statement

What is the value of $\frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + ...$ ?

Homework Equations

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I have no idea since it's neither a geometric nor arithmatic series

The Attempt at a Solution

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My Calculus purcell book tells me that it is e - 1 ≈ 1.718

But there are no ideas in it.
Please help

 

[haruspex]

Do you know how to find the Taylor series of a function? If so, consider e^x.