Premium Only Content
![Tetrahedral Numbers: Sum of 'n' Consecutive Triangular Numbers: Proof](https://1a-1791.com/video/s8/1/K/t/Z/M/KtZMh.qR4e.1-small-Tetrahedral-Numbers-Sum-of-.jpg)
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!As32ynv0LoaIibBbOJ0HyyI1sOoEhw?e=VxJ3Yv
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/tetrahedral-numbers-proof
Related Videos:
Summations Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HyAqJRuDIRPUAvO_3ytXtu
Sum of the squares of "n" Consecutive integers - Simple Proof: https://peakd.com/hive-128780/@mes/sum-of-the-squares-of-n-consecutive-integers-proof .
------------------------------------------------------
SUBSCRIBE via EMAIL: https://mes.fm/subscribe
DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate
Like, Subscribe, Favorite, and Comment Below!
Follow us on:
MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes
MORE Links: https://linktr.ee/matheasy
Email me: contact@mes.fm
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
-
3:10:29
Math Easy Solutions
12 days ago $0.01 earnedMES Livestream 73: Agenda 2030 Deep Dive
3741 -
59:24
The Dan Bongino Show
4 hours agoThey Fell Right Into Trump's Trap (Ep. 2417) - 02/06/2025
657K1.17K -
47:26
The Rubin Report
3 hours agoBill Gates Makes ‘The View’ Crowd Go Quiet with This Chilling Warning
61K130 -
LIVE
CryptoWendyO
35 minutes agoXRP RUMOR: RIPPLE HAS A SECRET DEAL WITH TRUMP?!
69 watching -
2:02:40
Steven Crowder
5 hours agoHow USAID Spread Fake News with Your Tax Dollars & Trump Took Down Title IX
378K219 -
LIVE
TheAlecLaceShow
2 hours agoGuests: Alex Marlow, Rep. Cloud & Rep. Gill | No Men In Women’s Sports | The Alec Lace Show
212 watching -
52:02
PMG
17 hours agoHannah Faulkner and Pastor Mark Driscoll | WAKE UP CHURCH
5.75K -
2:07:17
Matt Kohrs
13 hours agoMAX DEGEN TILT!!! (New Highs Incoming!) || The MK Show
60.5K3 -
55:35
Grant Stinchfield
2 hours ago $2.59 earnedDemocrats Fight Against Trump is a Losing Battle as the Swamp Drains Itself
28.2K11 -
1:28:55
The Shannon Joy Show
3 hours ago🔥HUGE Victory for Sanity - Trump Signs Executive Order Banning Trans Males From Women’s Sports! With Special Guest Alex Newman!🔥
34.4K5