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  "body": "\n## Statement\n\nLet $n$ and $r$ be natural numbers with $r \\le n$.\nThen\n$$\\sum_{i=r}^{n} \\binom{i}{r} = \\binom{n + 1}{r + 1}.$$\n\n## Remarks\n\nFor $r = 1$ it gives $1 + 2 + \\dots + n = \\binom{n+1}{2} = \\frac{n(n+1)}{2}$.\nCombinatorial proof: classify the $(r+1)$-subsets of $\\{1, \\dots, n + 1\\}$ by their largest element $i + 1$. The other $r$ elements come from $\\{1, \\dots, i\\}$.\nIn [[Pascal's triangle|05DME4TZ3K]] the summands lie on a diagonal, and the result lies below the end of the diagonal. This shape is the reason for the name.\n\n## Explanations\n\n### L1 human\n\nAdd the entries of [[Pascal's triangle|05DME4TZ3K]] along a diagonal, from the edge downward.\nThe total is the entry just below and to the side of the last one, so the picture looks like a hockey stick.\n",
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