Thread: Making change

I have to figure out all of the ways to make change for a dollar. I know that it is equal to the product of the geometric series for each of the coins, or (1/(1-x))(1/(1-x^5))(1/(1-x^10))(1/(1-x^25))(1/(1-x^50)), but I am stuck there. When I multiplied it out, the highest term I got was x^19, so I don't know what to do. Is there an easier way to do this problem or a way to actually find the answer?

1) Are you SURE that's the right construction? Why would a finite dollar bill need the product of five infinite series?

2) You just multiplied something wrong. Where would the x^50 go?

Originally Posted by TKHunny

1) Are you SURE that's the right construction?

This is a follow-up to the following post.
http://www.mathhelpforum.com/math-he...binatorix.html

I see. The finite construction simply has fewer cases but produces the same result for exponents less than 101.