A woman labels the squares of a very large chessboard 1 through 64. On each square k, the woman puts 2^k grains of rice. How many more grains of rice are placed on the 10th square than on the first 9 squares combined?
This is not that difficult by finding and adding the individual terms; however, you can use the formula for the
sum of a finite geometric series: Sum = a1 · (1 - rn) / (1 - r)
where a1 = 2 and r = 2: Sum = 2 · (1 - 29) / (1 - 2) = 1022
Compare this to: 210 = 1024
