Thanks for this very good explanation. However, I think I saw a proof done by using the method of differences. It would be good to compare and contrast which method is better. Keep up the great work you are doing 👍.
@@PrimeNewtons ua-cam.com/video/aI0M4XRiz4Ih/v-deo.htmlttps://ua-cam.com/video/aI0M4XRiz4Ih/v-deo.htmlttps://ua-cam.com/video/aI0M4XRiz4I/v-deo.html This is one link. There are more. I will look for them.
Oh I see. This is not mathematical Induction. It is deriving the formula itself. Mathematical Induction is what you use to prove that the formula is always correct.
If you compute the sum from r = 1 to n of Σ(r + 1)³ - Σr³ in two different ways, you can deduce the formula for Σr². Hint 1: Σ (r + 1)³ - Σr³ = Σ3r² + Σ3r + Σ1 Note: Σ1 = n and Σr = n(n + 1)/2. Hint 2: Σ(r + 1)³ - Σr³ = (n + 1)³ - 1³
![2^n is greater than n^2. Strategy for Proving Inequalities. [Mathematical Induction]](http://i.ytimg.com/vi/UE009vD3PEI/mqdefault.jpg)
![2^n is greater than n^2. Strategy for Proving Inequalities. [Mathematical Induction]](/img/tr.png)
![Prove that 11^n - 4^n is divisible by 7 for any natural number, n. [Mathematical Induction]](/img/n.gif)
Brilliant, as always! Thank you so much 👍
Greetings from Spain 🇪🇸
Thank you!
thank you for making math more understandable to me!
awesome! thanks so much for teaching me
Thanks Sir 👍
Thanks for this very good explanation. However, I think I saw a proof done by using the method of differences. It would be good to compare and contrast which method is better. Keep up the great work you are doing 👍.
I must confess I don't know what the method of differences is. Please share a link to it.
@@PrimeNewtons ua-cam.com/video/aI0M4XRiz4Ih/v-deo.htmlttps://ua-cam.com/video/aI0M4XRiz4Ih/v-deo.htmlttps://ua-cam.com/video/aI0M4XRiz4I/v-deo.html
This is one link. There are more. I will look for them.
@@PrimeNewtons ua-cam.com/video/OpA7oNmHobM/v-deo.html
Oh I see. This is not mathematical Induction. It is deriving the formula itself. Mathematical Induction is what you use to prove that the formula is always correct.
@@PrimeNewtons ua-cam.com/video/Xj2ndT-AoMw/v-deo.html
These are enough to give you an understanding of the difference method.
If you compute the sum from r = 1 to n of
Σ(r + 1)³ - Σr³ in two different ways, you can deduce the formula for Σr².
Hint 1: Σ (r + 1)³ - Σr³ = Σ3r² + Σ3r + Σ1
Note: Σ1 = n and Σr = n(n + 1)/2.
Hint 2: Σ(r + 1)³ - Σr³ =
(n + 1)³ - 1³
Sir, solve inequality