SOLUTION: I need help on this last problem! 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 t

Question 29590: I need help on this last problem!

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.
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?
Thank you a ton!!!
Answer by josmiceli(6786) (Show Source):
You can put this solution on YOUR website!
There are 64 squares
the farmer put 1 grain in a corner square
2 in the next,
4 in the next,
8 in the next
let g = total number of grains
let n = number of squares
the rule is
g = 2^0 + 2^1 + 2^2 + 2^3 + . . . + 2^n
so after, let's say 6 squares, the number of grains on the checkerboard is

(anything to the 0 power is one)

the total is 63
the totals are always 2^(n+1) - 1
so if n = 64

and the sum g is

to the limits of my calculator, I get
3689348815 . . . and 10 more decimal places or