An investigation of the series
1 - 1/2 + 1/3 - 1/4 + 1/5
I have not shortened or abbreviated this series in any way so far (I use abbreviated as being similar to the following abbreviation of the definition of e: lim as n goes to infinity of (1+1/n)^n).
We observe that the natural log of the limiting value of this series is equal to 2. That is, if we take e to the power of this number, we get exactly 2. We also see that if we reverse which terms are added and which are subtracted, we get the natural log of 4.