Premium Only Content

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
-
3:09:45
Math Easy Solutions
6 days ago $0.14 earnedMES Livestream 96: Who Runs the World Deep Dive
5621 -
6:17:39
SpartakusLIVE
8 hours ago#1 All-American HERO delivers JUSTICE and LIBERTY to the streets of Verdansk
45.9K -
51:22
IsaacButterfield
8 hours ago $1.85 earnedAustralia Bans Kanye & Trump To Host UFC At The White House
10.7K10 -
1:58:26
JustPearlyThings
8 hours agoModern Women Are Saying NO To Independence Day | Pearl Daily
128K130 -
1:43:32
Barry Cunningham
7 hours agoTHE PRESIDENT TRUMP WHITE HOUSE FIREWORKS DISPLAY AND INTERVIEW WITH GENERAL MICHAEL FLYNN
46.8K30 -
31:54
Iggy Azalea
4 hours ago $4.00 earnedPlaying a lil blackjack on my casino, Mother.land
37.8K9 -
25:45
Scary Mysteries
20 hours agoThe Alphabet Murders: Rochester’s Eerie Triple Tragedy
16.1K7 -
12:59
Machete Gaming
2 days ago $2.12 earnedI HATED FC25… But Then I Tried THIS
21.1K1 -
3:39:00
VapinGamers
7 hours ago $1.74 earnedFortnite Tourney Practice with DJSkids24 - Trying to Get Gouder Like My Spelling - !rumbot
17.4K1 -
11:25:22
ZWOGs
13 hours ago🔴LIVE IN 1440p! - Splitgate 2, Fortnite Practice, VR Games, and More! - Come Hang Out!
24.7K2