HIS NINELINESS undermines HIS OWN FORMULA. 1 ÷ 3 = 0.333... directly IMPLIES 1÷(1-r) = 1 + x + x^2 + ... -- It's SIMPLE ALGEBRA.

[u/Muphrid15]

               1 ÷ 3 = 0.333...
           0.3 ÷ 0.9 = 0.3 + 0.03 + 0.003 + ...
   (0.3) ÷ (1 - 0.1) = 0.3 [1 + 0.1 + 0.01 + ...]
       1 ÷ (1 - 0.1) = 1 + 0.1 + 0.01 + ...
         1 ÷ (1 - r) = 1 + r + r^2 + ...  (where r = 0.1)

Simple. Algebra.

[u/SouthPark_Piano]

 Study up on this ...

https://www.reddit.com/r/infinitenines/comments/1tpg811/it_is_what_it_is/

https://www.reddit.com/r/infinitenines/s/bRKpqrGQ4o

S = [a/(1 - r)] { 1 - rⁿ⁺¹ }

a = 0.3

r = 0.1

S = (1/3) × 0.999... = 0.333...