an Indian Legend tells the story of a king who lost a game of chess when he lost the can't access opponent what you wanted as a reward is a phone and said he wanted the king to place one grain of rice on the first square of the chess board to on the second square for on the third square and so on doubling the amount of rice and each square
c)how many grains of rice should be placed on the 64th square of the board give the answer in standard form to 3 significant figures
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Answer:
18446744073709551615 grains of rice
Step-by-step explanation:
Let
'a' be the first term in the series
'r' be the common ratio
'n' be the number of terms in the series
and let 'S' be the sum of the series.
We have,
S=a+ar+ar^2+ar^3+ar^4+⋯+ar^(n-1) - (1)
rS=ar+ar^2+ar^3+ar^4+⋯+ar^(n-1)+ar^n - (2) Subtracting (1) from (2), we get
rS-S=ar^n-a
S(r-1)=a(r^n-1)
S=a(r^n-1)/(r-1)
In our chess problem, a = 1, r = 2 and n = 64. Hence, we get
S=2^64-1=18446744073709551615
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