Question

The inventor of the chess board suggested a reward of one grain of when for the first square, 2 grains for the second, 4 grains for the third and so on, doubling the number of the grains for subsequent squares. How many grains would have to be given to inventory? (There are 64 square sin the chess board).

Answer 1

Required numbers of grains
`=1+2^(1)+2^(2)+2^(3)+...` to 64 terms
`=1+(2^(1)+2^(2)+2^(3)+...2^(63))`
`=1+(2(2^(63)-1))/((2-1))=(1+2^(64)-2)=(2^(64)-1)`.