What will this man's total income be for working 29 days ?

Question

Suppose you go to a company that pays 0.02 for the first day, 0.04 for the second day, 0.08 for the third day and so on. If the daily wage keeps doubling, what will your total income be for working 29 days ?

Total income = ?

Answer 1

it's the sum of a geometric series

common ratio = r = 2

1st term = a1 = 2 cents

general formula is

sn = an(r^n-1)/(r-1)

s29 = 2(2^29- 1)/(29-1)

= (1/14)(536,870,911)

= 38,347,922.2 cents

=about $383,479.22 for 29 days

= far more than you might have guessed