Respuesta :
Answer:
2^64. I know 2^20 is 1048576. Cube that and multiply by 16 or grab a calculator. I'm too lazy to solve this.
The time taken to count all the grain due to him is [tex]2^{64}-1[/tex] or 18,446,744,073,709,551,615 sec .
What is Geometric Progression?
Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
What is sum of Geometric Progression?
. The sum of infinite, i.e. the sum of a GP with infinite terms is [tex]S_{∞} = \frac{a}{(1 - r) }[/tex]such that 0 < r < 1.
The formula used for calculating the sum of a geometric series with n terms is Sn = [tex]\frac{a( r^{n} -1 )}{(r - 1)} ,[/tex] where r ≠ 1.
According to the question
A chess board has 64 squares and all had been filled with grain
1st squares of chess board has grain = 1 = [tex]2^{0}[/tex]
2nd squares of chess board has grain = 2 = [tex]2^{1}[/tex]
3nd squares of chess board has grain = 4 = [tex]2^{2}[/tex]
4nd squares of chess board has grain = 8 = [tex]2^{3}[/tex]
so on ..
As this is an Geometric Progression
Where
First term (a) = 1
common ratio (r) = 2
Number of terms = n = 64
Now,
it took just 1 second to count each grain ,
Time taken to count all the grains
By using formula of sum of Geometric Progression
Sn = [tex]\frac{a( r^{n} -1 )}{(r - 1)} ,[/tex] where r ≠ 1.
substituting the values in formula
S₆₄ = [tex]\frac{1( 2^{64}-1 )}{(2-1)} ,[/tex]
S₆₄ = [tex]2^{64}-1[/tex]
S₆₄ = 18,446,744,073,709,551,615
Hence, The time taken to count all the grain due to him is [tex]2^{64}-1[/tex] or 18,446,744,073,709,551,615 sec .
To know more about Geometric Progression and sum of Geometric Progression here:
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