Tetrahedral Numbers: Sum of 'n' Consecutive Triangular Numbers: Proof

In this video I go over tetrahedral numbers and provide a proof of their formula using mathematical induction. This video was requested by Dominic from Strode College in the UK, and is a good follow-up from my earlier video on the sum of consecutive integers. A tetrahedral number is a number that can be visually represented as 3 sided pyramid, that is a tetrahedron. For example the numbers 1, 4, and 10 can all be visualized as a stack of balls in a tetrahedron pattern. In fact, the tetrahedron is just the sum of consecutive "triangular numbers", which are numbers that can be represented by an equilateral triangle. I cover triangular or triangle numbers as well, and show that their formula is the sum of n consecutive integers. Finally, I use the triangle number formula as well as the principle of mathematical induction to prove the formula for a tetrahedron number. This was the first time I had learned about tetrahedron numbers so this was an interesting topic to cover. If you have any other video requests please let me know and I may cover it! The topics covered as well as their timestamps are listed below. Introduction: 0:00 Topics to Cover: 0:45 1. Shoutout to Dominic from Strode College: 1:22 2. Tetrahedral Numbers: 2:26 3. Triangular Numbers: 7:56 Formula for a Triangular Number: 8:42 Visualizing the Triangular Number Formula: 10:33 4. Formula for a Tetrahedral Number: 13:51 Proof by Mathematical Induction: 17:37 Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIibBbO... View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/te... Related Videos: Summations Playlist:    • Summations   Sum of the squares of "n" Consecutive integers - Simple Proof: https://peakd.com/hive-128780/@mes/su... . ------------------------------------------------------ Become a MES Super Fan!    / @mes   DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps