SOLUTION: Which pays more over the course of 10 days - $100 per day for the 10 days or one dollar the first day, $2.00 the second, $4.00 the third, $8.00 the fourth, etc., up to and includin

Question 550985: Which pays more over the course of 10 days - $100 per day for the 10 days or one dollar the first day, $2.00 the second, $4.00 the third, $8.00 the fourth, etc., up to and including the 10th day?
Please help
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
100 a day for 10 days gets you 1000 dollars.
start with 1 dollar for the first day and double it each day to get:
day 1 = 1
day 2 = 2
day 3 = 4
day 4 = 8
day 5 = 16
day 6 = 32
day 7 = 64
day 8 = 128
day 9 = 256
day 10 = 512
add all these up and you get 1023
you make more money with the doubling and the longer you go (the greater the value of n), the more money you will make.
fyi:
the formula for the doubling of the money each day is a geometric progression given by:
Sn = a(1-r^n)/(1-r)
a is the first value which is 1.
r is the ratio which is 2 (money doubles each day).
n is the number of days.
assuming 10 days, this formula gets you:
Sn = 1*(1-2^10)/(1-2) which equals:
1*(1-1024)/(-1) which equals:
-1023/-1 which equals:
1023.

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