We have 2,300 players at the start of the computer game. The game eliminates 1/2 of the players in every round. So after the first round we have: 2,300 * 1/2 = 1,150 players left. And after the 2nd round: 2,300 * 1/2 * 1/2 = 2,300 * (1/2)^2 and so on. And the function of the players eliminated in each round: f ( n ) = 2,300 * ( (1/2)^1 + (1/2)^2 + ....+ ( 1/2 )^n ) where n is the number of the round. The second part is the sum of the geometric sequence: a 1 = 1/2, q = 1/2: S n = 1/2 * (( 1/2)^n - 1 )/ ( 1/2 - 1 ) = - ( ( 1/2)^n - 1 ) = = 1 - (1/2)^n Answer: f ( n ) = 2,300 * ( 1 - (1/2)^n ).
