math problem

If I say I will give you a penny on the first day, 2 pennies on the second day, 4 pennies on the third day, and I just keep doubling and do this for a month, How much money would you have at the end of the month???

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  1. sum = 1+2+4+8+16+ ...
    = 2^0 + 2^1 + 2^2 + 2^3 + ... 2^30

    this is a geometric series
    = a(r^n - 1)/(r-1)
    = 2(2^30 - 1)/(2-1)
    = 2 147 483 646 pennies
    = $ 21 474 836.46

    (check my arithmetic)

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  2. Over 10 million

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