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 ).
