Sum of First N Cubes Equals Square of 1+2+3+...+n | Number Theory

preview_player
Показать описание
The sum 1^3 + 2^3 + 3^3 + ... + n^3 is equal to (1+2+...+n)^2. Amazing! In today's number theory video lesson, we'll prove this wonderful equality using - you guessed it - induction!

The sum of cubes and the sum of squares are cool, but the sum of cubes and the square of a sum is an even cooler pair!

I hope you find this video helpful, and be sure to ask any questions down in the comments!

+WRATH OF MATH+


Follow Wrath of Math on...

  1. Wrath of Math
  2. wrath of math
  3. math lessons
  4. math
  5. education
  6. math video
Рекомендации по теме
Sum of first 0:12:34

Sum of first n cubes - Mathematical Induction

Sum Of Cubes 0:01:38

Sum Of Cubes I (visual proof)

Sum of cubes 0:02:41

Sum of cubes of first n natural numbers #maths #themathprofessor #video

Visual Proof for 0:01:40

Visual Proof for the Sum of the First n Cubes

Prove by induction, 0:09:03

Prove by induction, Sum of the first n cubes, 1^3+2^3+3^3+...+n^3

Sum of First 0:11:59

Sum of First N Cubes Equals Square of 1+2+3+...+n | Number Theory

100 Subscriber Special: 0:09:51

100 Subscriber Special: The sum of the first n cubes (proof by Induction)

The method of 0:03:59

The method of differences and sum of cubes of natural numbers

Find the sum 0:11:19

Find the sum of first n squares, difference equation approach, (ft. Max!)

Sum of First 0:02:51

Sum of First n Cubes (Algebraic and Visual Proof)

Sum of cubes 0:09:29

Sum of cubes of first n natural numbers | Class 11 Chapter 9 NCERT | e-Vidyalaya

Sum of cubes 0:04:53

Sum of cubes of the first 'n' natural numbers

Proof of sum 0:15:17

Proof of sum of cubes of the first n natural numbers

Sum of the 0:12:23

Sum of the Cubes of 'n' Consecutive integers - Simple Proof

Sum of first 0:00:58

Sum of first n cubes

Geometrical Way To 0:06:50

Geometrical Way To Prove The Sum of Cubes of First 'n' Natural Numbers | PJ Exclusive |Pra...

Sum of Cubes 0:13:05

Sum of Cubes of First n Natural Numbers Derivation - Sequence and Series - Maths Class 11

Sum of cubes 0:12:30

Sum of cubes of the first n odd numbers

Summing cubes without 0:00:26

Summing cubes without words #phonk #phonkmath

# square root 0:04:20

# square root of sum of the cubes of first 'n' natural numbers//....

proof of Sum 0:05:57

proof of Sum of cubes of first n natural numbers by mathematical induction

232.Sum of Squares 0:08:43

232.Sum of Squares and Cubes of first n Natural Numbers 232

Trick | Sum 0:06:35

Trick | Sum of Cubes | First 'n' Natural Numbers | Natural Number Series - By ZOHEB SIR

Sum of cubes 0:12:43

Sum of cubes of 1st n natural numbers

Комментарии
Автор

Beautiful, this proof will help me for my class, patterns for Dr. Gannons triangle: related to 1^3 + 2^3+3^3++++ = a perfect square value, thank you.

juanjaimescontreras
Автор

Very well done! In your opinion, is this a "what a funny coincidence" kind theorem, or a "deep meanings are revealed" kind? It feels like the former to me, but it's still a nice example of how to do an induction proof.

mattkilgore
Автор

The usage of the board is insane ! Congratulations

antoine
Автор

Thank you soo much we just needed to used that formula n(n+1)/2

samiaakram
Автор

Oh, I just needed to use this n(n+1)/2 formula while prooving... Thank you! :)

katiasavina
Автор

did not know about this formula, my book formula looks different, this is much easier, thank you

aryamanjha
Автор

If you're watching this reply me with your age

ayushjaiswal
Автор

I got asked this in an interview question. I proved it by induction like you did but they asked for a geometric interpretation? Can anyone who has one reply to this comment?

finlayhutchinson