Problema Solution
Suppose you are offered two different prizes the first prize is $250,000 a week for four straight weeks for a total of $1 million for the second prize imagine if you will a chess or checkers board and you place a penny on the first board space then for the second space you placed two pennies and on the third space you place four pennies you continue this pattern until you cover the whole board which price do you keep and why
Answer provided by our tutors
the first prize is: $1,000,000.00 = (10^6)*(10^2) cents = 10^8 cents (since $1 = 100 cents)
the second prize is the sum of the first 64 terms (the chess board has 8*8 = 64 fields) of the geometric sequence: 1, 2, 2^2, 2^3...
a0 = 1
an = 2^n
S = 1*(1 - 2^63)/(1 - 2)
S = 2^63 - 1
2^63 - 1 = (2^4)^(63/4) - 1 > 16^(60/4) = 16^15 - 1 > 10^15
S > 10^15 > 10^8 thus the second prize is bigger and you should keep the second prize.