First, we can eliminate steps 3 & 4 from the example. These are not relevant and require extra calculations to get the same results.

Second, “Finally, divide 0.78539 by .00039 to get your resolution. In this case, the resolution of this machine axis’ configuration is: 2013.821 steps per inch.” is wrong. The figure 0.00039 was derived by dividing 0.79539 by 2000, so dividing the same 0.79539 by 0.00039 will always give you the original divisor 2000 (or close to it when you truncate, 2013.821).

Instead, here is a more direct approach:
1) Calculate the gear ratio (Driven gear / Driving gear) (72 teeth / 15 teeth = 4.8)
2) Calculate motor steps per output shaft revolution (gear ratio * steps per motor revolution) (4.8 * 2000 steps = 9600 steps)
3) Convert Pitch Diameter to Circumference. (P.D. * pi) (1.2 inch * pi = 3.7699 inch). This is the linear distance traveled for each revolution of the output shaft.

Now the magic…
4) Steps per Inch = Steps per output shaft revolution / Pitch Circumference (9600 steps / 3.7699 inch = 2546.479 steps per inch) (** 2000 steps = .78539 inch. That’s almost 80%, so the missing 21.5% is a little more than 500 steps, 546.479 to be exact, for a total of 2546.479 steps per inch. This is a bit more than the 2013..821 in the example. **)
5) Resolution, or Inches per Step = Pitch Circumference / Steps per output shaft revolution (reverse the terms in step 4, 3.7699 Inch / 9600 step = 0.0003927 inches per step) (or invert step 4 result, 1 / 2546.479 steps per inch = 0.0003927 inches per step).