Question

The inventor of the chess board suggested a reward of one gram 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 subsequent squares. How many grins would to be given to inventor? ( There are 64 squares in the chess board).

Answer 1

No. of grains for the first square = 1 ,the second square = 2 ,the third square = 4 and so on.

These no. of grains form a G.P. as $2^0,2^1,2^2,2^3,...,2^{63}$

So the first term of G.P. is $a=1$ and common ratio is $r=2$ no. of terms in this G.P. is 64.

Since sum of n terms of G.P. $=\frac{a(r^n-1)}{r-1}=\frac{1(2^{64}-1)}{2-1}=2^{64}-1$