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Mathematics, 24.09.2019 00:10 harleycochran2ovyt3n
In a well known story the inventor of the game of chess was asked by his well king what reward he desired. "oh, not much, your majesty", the inventor responded, "just place a grain of rice on the first square of the board, 2 on the next, 4 on the next, and so on, twice as many on each square as on the preceding one. i will give this rice to the poor." (for the uninitiated, a chess board has 64 squares.) the king thought this a modest request indeed and ordered the rice to be delivered.
let f(n) denote the number of rice grains placed on the first n squares of the board. so clearly, f(1)=1, f(2) = 1+2 = 3, f(3)= 1+ 2 + 4 =7, and so on. how does it go on? compute the next two values of f(n): f(4) = ~ f(5) = ~
ponder the structure of this summation and then enter an algebraic expression that defines
f(n) = as a function of n. supposing that there are 25,000 grains of rice in a pound, 2000 pounds in a ton, and 6 billion people on earth, the inventor's reward would work out to approximately 3(10)^17 tons of rice for every person on the planet. clearly, all the rice in the kingdom would not be enough to begin to fill that request. the story has a sad ending: feeling duped, the king caused the inventor of chess to be beheaded.
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In a well known story the inventor of the game of chess was asked by his well king what reward he d...
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