In the NCAA Men’s Basketball Tournament, 64 teams are initially paired off. Before the recent changes, a champion was crowned through a series of single-elimination games.

(a) Write a geometric sequence whose sum determines the number of games that must be played to determine the champion team.
(b) How many games must be played to produce the champion?
(c) Generalize parts (a) and (b) to a tournament where 2ⁿ teams are initially present.
(d) Discuss a quick way to determine the answers to parts (b) and (c), based on the fact that each game produces one loser, and all teams except the champion lose one game.