   SEARCH HOME Math Central Quandaries & Queries  Question from Jerrie, a student: Patti saved pennies for 10 days.  The first day she saved 1 cent.  Every day after that she saved twice as much as the day before.  How much money did Patti save altogether? Hi Patti.

Write out what is happening:

First day: 1 cent = 1 cent total

Second day: 1 cent + 2 cents = 3 cents total

Third day: 1 cent + 2 cents + 4 cents = 7 cents total

Fourth day: 1 cent + 2 cents + 4 cents + 8 cents = 15 cents total

Each day, the amount Patti adds is two times the previous day. So on day number D, she adds 2D cents.

Notice also that each day, the amount she is adding is one more than the total for the previous day. For example, the total on the third day is one cent less than the amount she adds on day four.

So the amount she has in total on the 10th day is one cent less than the amount she would add on day eleven.

Can you find out what 211 - 1 is equal to?

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.