Can you follow the following mathematical derivation?

A geometric series has the form 1 + x + x(2) + ,,, x(n)

Suppose you want to find the vaue of s = 1 +3 +9 +27 + 81, a geometric series for x = 3.

Imagine a tournament for the board game Monopoly. Each game has 3 players and only the winning players in each round go on to the next one. If 81 is the number of games in the first round, then each previous number is the number of games in the following round. Therefore s equals the total number of games in the tournament.

We can look at the situation as follows. Since there are 81 3-player games in the first round, the total number of players in the tournament is 3×81 = 243. In order to go from 243 starting players to to a single champion, 242 players must be eliminated. Since 2 players are eliminated in each game, the total number of games must be 242/2=121, so s = 121.