I was looking through some of my older questions, when I came across this crazy integral I posted.
$\int\limits^{2}_{1}\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}dx$
I had approximated it at $0.871327768063$. Reading the comments, I noticed C-Ram said determining the convergence of the integral seems like a more interesting problem and I agree.
This is still way over my skill level and I don't know how to even attempt proving convergence but I am still curious about how it could be done.
