 # John L's Formulas – Chapter One

### Page 4. Continuing from Page 2, our equation – X=n^(1/(n-1)) – does not appear to "compute" when n = 1, and X has to be inferred from a graph. A rough graph in the following figure shows X to be between 2 and 3 when n = 1. This graph was sketched based on certain values for n. When a wide range of n values (also shown in the figure) was fed into the equation to generate corresponding values for X – with the use of the Equation Solver program – X was seen to approach e as n approached 1 from both directions. And it so happened that when n was given the value of 1, no value for X was generated by the program at all. All that was shown was simply "%." One could tentatively conclude that X = e when n = 1 in this equation, but one would think that an absolute proof needs to be shown by a solid mathematical methodology and certainly should not be inferred as shown here. Analysis of the data and the graph generated at WebGraphing.com shows a discontinuity at n = 1. Such a discontinuity is termed a "hole" and is shown as such on a graph where X would otherwise be e.  