Hey, my name is Kanishk (student, grade9) I was wondering if you help me on this question: I recieve 1 penny the 1st day, 2 pennies the 2nd day, and my salary is doubled everyday for 30 days. How much money will I have by the end of the 30 day time period? (Is there a way of solving this problem without a chart?) Hi Kanishk,
The total amount that you receive is
The key to finding a nice expression for this sum is to first multiply both sides by r to get = a + ar + ar^{ 2} + ar^{ 3} + ar^{ 4}+ ... + ar^{ 29}  ar  ar^{ 2}  ar^{ 3}  ar^{ 4}  ar^{ 5}  ...  ar^{ 30} = a  ar^{ 30} Now evalute this expression when a = 1 and r = 2. Cheers,Penny
