Question 34054
according to the question
"place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square."

you will know the general equation is:
number of square = 2 ^ (number of square -1)
assume number of square = x
then, yields the equation
x = 2^(x-1)

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below shows verification:
if x = 1
1 = 2^(1-1) = 2^0 = 1
2 = 2^(2-1) = 2^1 = 2
3 = 2^(3-1) = 2^2 = 4
does this make sense?  if yes, let's keep going
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a)How much money would Mr. Brown have to put on the 32nd square?
that means x = 32
x = 2^(x-1)
32 = 2^(32-1) = 2^31 = 2,147,483,648 pennies




b)How much would the traveling salesman receive if the checkerboard only had 32 squares?

= 2^31 + 2^30 + 2^29 + ...... + 2^0
use a calculator to calculate



c)Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman?

= 2^63 + 2^62 + 2^61 + ...... + 2^0
use a calculator to calculate