Uploaded September 2026 | Updated September 2026, 2 weeks ago
Finite Sums of Positive Integers
In this video, we show an animation of a visual proof of the formula for the sum of the first n positive integers. This differs slightly from the more classic version (using two triangular stacks to form a rectangle). Instead, we use two triangular stack and a diagonal line to produce a formula for the sum.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
To see more related proof, check out these videos:
youtu.be/mZujswzs7Qg?si=bulQkTRvlSy9MCrR
youtu.be/eHbtc50-qXo?si=ztvGFf1G-dLzr-m3
I learned of this visual from Bob Palais: web.archive.org/web/20190607085735/http://www.math.utah.edu/~palais/sums.html
#math #manim #sumformula #naturalnumbers #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #finitesums #sums #shorts #triangularnumbers
To learn more about animating with manim, check out:
https://manim.community
Finite Sums of Positive Integers
In this video, we show an animation of a visual proof of the formula for the sum of the first n positive integers. This differs slightly from the more classic version (using two triangular stacks to form a rectangle). Instead, we use two triangular stack and a diagonal line to produce a formula for the sum.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
To see more related proof, check out these videos:
youtu.be/mZujswzs7Qg?si=bulQkTRvlSy9MCrR
youtu.be/eHbtc50-qXo?si=ztvGFf1G-dLzr-m3
I learned of this visual from Bob Palais: web.archive.org/web/20190607085735/http://www.math.utah.edu/~palais/sums.html
#math #manim #sumformula #naturalnumbers #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof #mathshorts #mathvideo #finitesums #sums #shorts #triangularnumbers
To learn more about animating with manim, check out:
https://manim.community
