The inventor of the chess board suggested a reward of one grain of wheat 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 inventor? (There are `64` square in the chess board).

Explanation

Given,

Number of grains for the `1st` square `= 1`

`2nd` square `= 2`

`3rd` square `= 4`

It continues to to `64th` square

G.P. sequence `=2^0, 2^1, 2^2, 2^3,..., 2^63`

`a=1, r=2, n=64`

`S_(64) =(a(r^64−1))/(r-1)=(1(2^64−1))/(2-1)=2^64−1`

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