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You offer to do the dishes for your family for the next month.This month has only 31 days. You suggest that they can pay you in one of three ways:

A. $0.50 each day.(I already did this;=$15.50 a month.
B.$0.10 the first day,$0.20 the second day,$0.30 the third day,and so on.
C.$0.01 1st day,$0.02 2nd day,$0.04 3rd day,doubling each time.

Which rate of pay would be best for you?

I already know the 1st and 2nd choices,but to calculate the 3rd one one by one seems a bit overrated.
So...I was wondering if there is a sort of pattern for doubling like in the third choice?


  • math -

    You get .01 for the first day, .02 for the second, then keep doubling. However, they might fire you after the first dozen days or so.

    It is a logarithmic progression in contrast to the second, which is an arithmetic progression.

    1 + 2^30 = ?

    In currency terms = .01 + .02 + .04 + .08 + .16 + .32 + .64 + 1.28 + 2.56 + 5.12 + 10.24 + 20.48….

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