Some years ago I found an expository article devoted to proving Newton's binomial theorem, which says that if $n$ is any real (not necessarily positive and not necessarily integral) number, and $|x|<1,$ then $$ (1+x)^n = \sum_{k=0}^\infty \binom n k x^k = \sum_{k=0}^\infty \frac{ \overbrace{n(n-1)(n-2)\cdots(n-k+1)}^{k \text{ factors}}}{k!} x^k. $$ When $n$ is a nonnegative integer, all except $n+1$ terms vanish; otherwise none of them do unless $x=0.$
I thought this was in the American Mathematical Monthly, but via Google Scholar I can't find it there, nor any article in any publication matching that description.
Where is this?