Triangular Numbers Modulo 3 (visual proof)

[@solaokusanya955]

Amazing

[@oddlyspecificmath]

Okay...I'm rewatching at least once; I got distracted, reminded of those rearrangement puzzles where a bit disappears and you're supposed to explain where it went 😅

[@BintangPagar-l2r]

Please proof the difference to product identities II sina-sinb=...

[@carlkarl]

Hmm can u do 1+2+3+4+......infinite =-1/12

[@mathematicsman7454]

Don't copy the repeating news

[@carlkarl]

@@mathematicsman7454 didn't got it, but my maths teacher told me that proof when I was in 9th grade so just asking u to do it if it's possible, u can deny the request, I'll accept it

[@MathVisualProofs]

It’s not really true. I can be shown if you use Cesaro summation on a particular series, but because it is not 100% correct it will be impossible to find a visual proof.

[@robologo]

You lost me at 00:12 I dont understand that equation. Idk what it means that the k is at the bottom of the T.

[@MathVisualProofs]

That’s the definition of the number T_k. k is any positive integer and it tells you where to stop adding. So T_5 would be 1+2+3+4+5

[@solaokusanya955]

But I don't understand the " 3 " part

[@MathVisualProofs]

What do you mean?

[@solaokusanya955]

@@MathVisualProofs I don't understand the part where you made. 3 the coefficient and how you separated 2k +1 and k

[@MathVisualProofs]

@@solaokusanya955 So 3k+1 splits into 2k+1 + k, so I decomposed the base dots into two sets. Then, I formed a trapezoidal array using those two measurements (2k+1 by k) and that trapezoid was able to fit "3" times around the array. This means I have 3 copies of the resulting trapezoidal array. The trapezoidal array is then built as the difference of two triangular arrays, and so that's where the rest of the formula came from.

[@SirP-rd5yh]

A big fraud.

[@SirP-rd5yh]

A cheap way of explaination.

[@SirP-rd5yh]

low quality teacher