Question 65064
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer: 
Show work in this space 
The 1st square has 2^0=1 cent
The 2nd square has 2^1=2 cents
So, the 32nd square has 2^31 cents
2^31=$21,474,836.48
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b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer: 
Show work in this space 
1+2+4+8+...+2^31
S(n)=(n/2)(1st term + last term)
S(32)=(32/2)(1+2147483648)=$34,359,7383.80
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c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer: 
Show work in this space 
1+2+4+....+2^63
S(64)=(64/2)(1+2^63)
=$2.951479052x10^18
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Cheers,
Stan H.