What is the better deal? Earning $1000 a day for the rest of your life or earning $.01 the first day and doubling it every day for the rest of yor life. How do you know?
depends how long you live
Suppose you work for 30 years
= 10950 days, ( you work 7 days a week, every day even Christmas)
amount earned = 10950(1000) = 10, 950,000 , not bad
amount of second plan
you have a geometric sequence
where a = .01, r = 2, n = 10950
amount = .01( 2^10950 - 1)/(2-1)= too big for my calculator
apprimation
let x = 2^10950
logx = 10950(log2) = appr 3296
x = 10^3296
amount = .01(10^3296) = 10^3294
which is a number like
10000.....00 , for 3294 zeros
They should have specified a more realistic and shorter time period.
It is estimated that there 10^18 grains of sand on earth
If the entire universe were filled with sand, it would be less than 10^3294