I find combinatoric algebra very non-intuitive. I'm talking about Pascal's Identity n≥r,
(n+1r)=(nr)+(nr−1).
I understand the tedious proof of the theorem but what's a trick for understanding combinatoric algebra in general? I can't eyeball and decompose a binomial without memorizing the formulas or doing tedious factorial multiplication and division.
It's never obvious how combinatoric algebra works:
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