Question

The inventor of chessboard was a very clever man.He asked the King, a reward of one grain of wheat for the first square,2 grains for the second, 4 grains for the third and so in. By doubling the number of the grains for each subsequent square,how many grains would have to be given? ??

Answer 1

Answer:

$Total \: number \: of \: grains = 2(2^{64}-1)$

Step-by-step explanation:

/* According to the problem given,

$Total \: number \: of \: grains (S) \\= 2+2^{2}+ 2^{3} + \cdot\cdot\cdot+2^{64}$

/* This sequence is clearly in G.P */

$First \:term (a) = 2$

$Common \:ratio (r) = \frac{a_{2}}{a_{1}}\\= \frac{2^{2}}{2}\\= 2$

$number\: squares \: on \:chess \:board (n) = 64$

$\boxed {\pink {S_{n} = \frac{a(r^{n} - 1}{(r-1)}}}$

$S_{64} = \frac{ 2 ( 2^{64} - 1)}{(2-1)}\\= 2(2^{64}-1)$

Therefore.,

$Total \: number \: of \: grains = 2(2^{64}-1)$

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