Question 353769
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) = 2^4-1 = 15___ ~ f(5) = 2^5-1 = 31___ 
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Ponder the structure of this summation and then enter an algebraic expression that defines
f(n) =2^n-1____ as a function of n.
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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 ____tons of rice for every person on the planet.
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# of grains = 2^64-1
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(2^64-1)grains/25000(grains/lb)/2000(lbs/ton)/6 million people 
= 1,537,228,673(tons per person) 
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Cheers,
Stan H.