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# Geometric Series and Sums : Checkerboard Story Problem - Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the ....

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CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown insisted on giving the man an award for his heroism.

So, the salesman said, "If you insist, I do not want much. Get your checker-board and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies." As he'd been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
How much money would Mr. Brown have to put on the 32nd square?
How did you solve it for the answer?

How much would the traveling salesman receive if the checkerboard only had 32 squares?
Again show me how you solved it.

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