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 2^D 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.