Question

Build Rate = houses + 1 / 10.
With 10 houses you have a Build Rate of 1.1 houses per month and every month you can use the rounded down build rate. For example this month you can build 1 house and not 1.1 with the result being that you now have 11 houses and a Build Rate of 1.2.

You start with 10 houses.

Determine a formula where you provide the number of months and it solves for the Build Rate.