Harmonic Sums and Divergence of Harmonic Series (visual proof)

This is a short, animated visual proof showing a formula for the sum of harmonic sums using triangular diagrams. As a bonus feature (watch until the end), we utilize this formula along with a theorem due to Ernesto Cesáro to prove that the Harmonic Series diverges. #math #manim #harmonicseries #harmonicsum #divergent #diverges #triangle #animation #theorem #pww #proofwithoutwords #visualproof #proof

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Music in this video:
Cold Blue by Astron

[marouaniAymen]

You did blow my mind, illuminate my memory and revived the love of math on me

[MyWissam]

nice, I like this example of a proof by contradiction.

[curtiswfranks]

I enjoyed this one a lot. I cannot wait to use it on one of my students.

[greedskith]

Prosthaphaeresis Formulas (trig product to sum) sir can you please help me with this pww i spent too much time but i cant crack it...

[thenewdworldfan]

This is not a complete visual proof, because you didn't prove the limits or even cesaro sums visually.

[Jack_Callcott_AU]

At 02:15 a much more elegant proof that the harmonic series diverges than the one usually given in textbooks. 🪃