Here is a cool sum. Is it possible to derive this closed form?.
I apologize for the wacky sums that did not pan out. As I said, I only had around 10 decimals places. It was safe to assume that closed forms like that were too good to be true
They came from that Inverse Symbolic Calculator. I rarely use it, so I was just playing around.
Anyway, try this one if you like. I think it is more amenable.