SOLUTION: This is my last question, Thanks for all your help everybody. 4) CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on

Question 39196: This is my last question, Thanks for all your help everybody.
4) 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 Crane came out and gratefully thanked the traveling salesman for saving his daughter�s life. Mr. Crane insisted on giving the man an award for his heroism.
So, the salesman said, �If you insist, I do not want much. Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat.� As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
a) How much wheat would Mr. Brown have to put on the 24nd square?
Answer:
Show work in this space.

b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Answer:
Show work in this space.

c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
Answer:

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a) How much wheat would Mr. Brown have to put on the 24nd square?
Answer:
Show work in this space.
1st square gets 2^0=1 grain
2nd square gets 2^1=2 grains
24th square gets 2^23 grains

b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Answer:
Show work in this space.
2^0+2^1+2^2+ .....+2^23
This is a geometric series with r=2 and n=24
The sum of the series is S(24)=[2^24-1]/[2-1]= 16777215

c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
Answer:
S(64)=[2^64-1]/[2-1]=1.84467441X10^19
Cheers,
Stan H.
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