Archive for May 2009

## Making Change for America

Guest post by Lee Newberg [but see Comment below]

I stumbled across an old Math Chat column of yours, which mentioned that the number of ways to make change for a dollar is the coefficient of $x^{100}$ in the Taylor expansion of

$\frac{1}{(1-x)(1-x^5)(1-x^{10})(1-x^{25})(1-x^{50})(1-x^{100})}$.

But I don’t see there, or anywhere on the web, the general formula for the number of ways c(n) to make change for n dollars.  In case you are interested, below I derive it to be:

$c(n) = (6 + 127n + 483n^2 + 672n^3 + 390n^4 + 80n^5)/6$.

Spending 1 trillion dollars with the federal stimulus means that Obama has

$c(10^{12})$=  13 333333 333398 333333 333445 333333 333413 833333 333354 500000 000001

ways to make Change for America. Continue reading ‘Making Change for America’ »