I ran across an interesting series. I looked at it and must admit, I do not even know where to begin. I tried playing around with it, but to no avail.
Here it is. Perhaps it isn't doable.
$\displaystyle \frac{1}{\ln(2)}+\frac{1}{\ln(2)\ln(3)}+\frac{1}{\ln(2)\ln(3)\ln(4)}+\cdots $
I ran this through Maple. It does appear to converge.
It gave me $4.934269949\dots$
Can this even be evaluated in some clever manner?