Suppose you want to make change for $100, using at least twenty one-dollar bills. How many ways are there to do this? (There are at least two different ways to attack this problem. One is to note that the factor in the

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Suppose you want to make change for $100,
using at least twenty one-dollar bills. How
many ways are there to do this? (There are at
least two different ways to attack this
problem. One is to note that the factor in the
generating function describing the one-dollar
bills is no longer 1 + x + x 2 + x 3 +
because we're not allowed to use zero or one
or two one-dollar bills any more. What is the
smallest power of x that can show up in this
factor? I suggest carefully writing out the first
few terms of the correct factor, and then
figuring out the correct expression to feed the
computer in place of 11-x .)
Transcribed Image Text:Suppose you want to make change for $100, using at least twenty one-dollar bills. How many ways are there to do this? (There are at least two different ways to attack this problem. One is to note that the factor in the generating function describing the one-dollar bills is no longer 1 + x + x 2 + x 3 + because we're not allowed to use zero or one or two one-dollar bills any more. What is the smallest power of x that can show up in this factor? I suggest carefully writing out the first few terms of the correct factor, and then figuring out the correct expression to feed the computer in place of 11-x .)
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