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 1 + 2 + 4 + 8 + 16 + ... where the sequence continues for 30 days. This is an example of a geometric series. A geometric series is constructed form a first term a and a number r, called the common ratio. The series is then a + ar + ar 2 + ar 3 + ar 4 + ar 5 + ... In your series a = 1 and r = 2 and the number of terms is 30 so the sum is given by S = a + ar + ar 2 + ar 3 + ar 4+ ... + ar 29 The key to finding a nice expression for this sum is to first multiply both sides by r to get rS = ar + ar 2 + ar 3 + ar 4 + ar 5 + ... + ar 30 and then subtract rS from S. S - rS = a + ar + ar 2 + ar 3 + ar 4+ ... + ar 29 - ar - ar 2 - ar 3 - ar 4 - ar 5 - ... - ar 30 = a - ar 30 Hence S = a (1 - r 30)/(1 - r) Now evalute this expression when a = 1 and r = 2. Cheers, Penny Go to Math Central