Question 74249
Here is the Answer...
 

a)To find out how many pennies are on the 32th square, simply evaluate 2^31 (we go to the n-1 term since we started off at n=0). Well it comes out to 2,147,483,648 pennies.
 If you want to verify, you can double 1 to 2, 2 to 4, etc until you get there.
 Divide this figure by 100 to get the value in dollars.
 
And he would pay $21,474,836.48 alone for the 32nd square 


b)To find the sum of any geometric series, i.e. how to find 1+2+4+8+...2,147,483,648, you would use the sum of a geometric series formula. If I have a series of n terms the sum is
 don't worry about a, we will ignore it, a=1 right now
 and r is the factor to go from term to term, in this case r=2 (we're doubling everything). 


And this means that there are a total of 4,294,967,295 pennies if 32 squares were filled.
 Divide this figure by 100 to get the value in dollars.
 
And if there were only 32 squares, then he would pay $42,949,672.95 

c)To find how many pennies would fill the entire board, use the same formula but with 64 squares
 

And there are 18,446,744,073,709,551,616 pennies needed to fill the entire board. Divide this figure by 100 to get the value in dollars. 

This means that he would have to pay $184,467,440,737,095,516.16 to the salesman.
 This Sales Man Is Veryy, SMART!! He Knew What he was Doing When He said just a small amount of pennies...