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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?

  • 0
    Looks unlikely to have a closed form to me, with the multiple logarithms and all.2011-12-03
  • 0
    It's easy to see that it indeed converges (by the Ratio Test, say).2011-12-03

1 Answers 1