1
$\begingroup$

I already posted this question on here.

After reading this post and the general solution for that case, I wondered if there is a closed form for the general solution for this sum:

$ \sum_{a_1=0}^\infty~\sum_{a_2=0}^\infty~\cdots~\sum_{a_n=0}^\infty\dfrac1{(a_1!+a_2!+\ldots+a_n!)} $

Any idea?

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ When $n = 2$, this equals approximately $4.91600919$. A good starting point would be finding a closed-form expression for that number. $\endgroup$
    – Nathaniel Johnston
    Commented May 17 at 2:13
  • 3
    $\begingroup$ I read your post at MathSE. A few commenters said this looks hopeless (I agree), and one said that people here at MO might be able to explain why this is so hard. I don't think anyone will be able to answer your question as posed. Nor am I confident that they can convincingly explain why it should be so hard (why is the Collatz problem hard?), but maybe you'd get better replies to the latter question. But is this an idle question? Or do you have some good motivation for asking? $\endgroup$
    – Todd Trimble ♦
    Commented May 17 at 2:41
  • 6
    $\begingroup$ We don't even know if $\sum1/(n!+1)$ has a closed form: oeis.org/A217702 $\endgroup$
    – ho boon suan
    Commented May 17 at 3:43

0

Reset to default

Browse other questions tagged or ask your own question.