Question

The inventor of the chessboard 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 grains for subsequent squares. How many grins would be given to the inventor?

Answer 1

Step 1: Analysing the problem

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 GP. as $20,21,22,23,...,263$

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

Step 2: Finding the number of grains

Sum of $n$terms of GP,

$\frac{a(r^n-1)}{r-1}=\frac{1(2^{64}-1)}{2-1}=2^{64}-1$

Therefore, the number of grains is $2^{64}-1$