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?

Guest Apr 8, 2022

#1**+1 **

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 = a_{1} · (1 - r^{n}) / (1 - r)

where a_{1} = 2 and r = 2: Sum = 2 · (1 - 2^{9}) / (1 - 2) = 1022

Compare this to: 2^{10} = 1024

geno3141 Apr 8, 2022