In month 1, we have 1 * C companies. In month 2, we have 1 * .978 * C companies. .978 is the survivorship rate, which is the inverse of the churn. In month 3, we have 1 * .978 * .978 * C companies.
Given that we are most keenly interested in how many company-months we rack up over time, we can solve for this with sum of an infinite geometric series. The formula is C / (1 - s) for s is the survivorship rate, or C / (churn).
Exactly like Gail said it was.
the survivorship rate, which is the inverse of the churn
More logical I think would be SR = (1-churn). Of course, .978 is close enough to 1.0 that it doesn't matter, and I don't understand how the grandparent arrived at 32 months.
Edit: your two formulas for total company-months also imply that sr = (1-churn), so maybe I'm missing something?
With this definition, a churn of 0.75 is a survivorship of 0.25.
You're perhaps being misled by the offhand phrase "the survivorship is the inverse of the churn"; in that sentence "inverse" is not being used in the mathematician's strict sense of "reciprocal", but in the more colloquial sense of "a thing that moves in the opposite direction from the previous thing".
None of us understand where 32 months came from.