



 
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 2^{11}  1 is equal to? Cheers,  


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