A combinatorial proof of the following relation: $$\binom{n+2}{3} = 1 \cdot n + 2 \cdot (n-1) + 3 \cdot (n-2) + \cdots + n \cdot 1$$
So one side is the number of ways to choose $3$ numbers from $n+2$ numbers and the other side I did like this:
2026-03-31 12:17:24.1774959444
Combinatorial proof of $\binom{n+2}{3} = 1 \cdot n + 2 \cdot (n-1) + 3 \cdot (n-2) + \cdots + n \cdot 1$
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