### A product rule for triangular numbers

#### by David Radcliffe

The nth triangular number is . It represents the number of dots in a triangular arrangement, with 1 dot in the first row, 2 dots in the second row, etc. (Image source: Wikipedia)

The triangular numbers satisfy many interesting properties, including a product rule:

This rule can be demonstrated visually by subdividing a triangle into smaller triangles. The following picture illustrates the case

.

Inspired by a question of James Tanton, I sought to find all sequences that satisfy this product rule. This problem has a lovely solution, and I encourage you to discover it for yourself. I will outline my solution in subsequent posts.

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[…] A product rule for triangular numbers. It turns out that triangular numbers satisfy the rule (and there’s a nice pictorial proof of this); are they the only such sequence? Share this:TwitterFacebookLike this:LikeBe the first to like this. Categories Uncategorized […]

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