find the ratio of amount of rice placed on a chessboard between first and second half of chessboard?

Question

I think the sequence for this is:

1, 2, 4, ...

I'm not sure what it means by first half of chessboard vs next half of chessboard. I'm assuming it is some kind of ratio?

Answer 1

Hint: In chess, the "first half" and "second half" refer to the top and bottom half respectively. So all you need to do is find $\sum_{I = 0}^{31} 2^I$ and $\sum_{I = 32}^{63} 2^I$ for the bottom and top half respectively.