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I just became curious about this sequence, so I tried several method to get exact value of the sum.
I know it converges, but I have no idea to calculate the exact value.
Is the value of $\sum_{n=1}^{\infty}\frac{1}{1+n!}$ already known, or does any nice method for it exist?

okw1124
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  • Did you try telescoping sum? Not sure if that works or not. Wolfram Alpha gives the value to be $1.02607....$ , and that looks like an usual number – Anonymous Sep 19 '20 at 09:47
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    Do you have any reason to suspect that there is some nice characterization of the answer? Most convergent sums do not have closed-form expressions for their limits. – Ben Grossmann Sep 19 '20 at 09:49

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