Have you ever needed to sum consecutive integers in a closed form? How do you proceed? There is a recursion that takes every know formula to calculate the next one using a lot of algebra, or you can take just the previous one with some arithmetics, no algebra needed! In this video, I show you this simple form, which nobody talks about, and provide a proof of why it works. Hope it helps you in your next sums!
This is my entry for the #SoME3 competition of math videos, those like #3blue1brown makes.
Not using Manim, only HTML-CSS-JavaScript animations.
00:00 Introduction - integer power sums
00:52 Some stange pattern
03:56 Sum of powers - the hard way
07:17 Practicing the hard way
08:21 Sum of powers - the easy way
13:06 Applying the miraculous method!