This is a short, animated visual proof showing how to find the sum of the first n triangular numbers (which themselves are sums of the first n integers) using stacks of tokens on three triangular stacks of squares.
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Here is a sum of squares visual proof using a similar technique:
• Sum of Squares II (visual proof)
This animation is based on a visual proof attributed to Richard K. Guy by Roger B. Nelsen in his first Proofs without Words compendium (I may receive a small commission at no cost to you for these affiliate links):
https://amzn.to/48mjeX1
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Watch video Tri-Nums Sums! (visual proof IV) online without registration, duration hours minute second in high quality. This video was added by user Mathematical Visual Proofs 23 March 2024, don't forget to share it with your friends and acquaintances, it has been viewed on our site 2,735 once and liked it 151 people.