Mathematical Induction

I explained how to prove a formula by induction.
You should try this if you get it.
1+3+5+...+(2n-1) = n^2

[blackredwhite]

The first video that was explained in human language, thanks you so much Dr. Newton

[josephparrish]

This is the first topic I remember studying in College Algebra so many many years ago. Fun!!

[skwbusaidi]

In the step
3k(k+1) + 6(k+1)
We can factor 3(k+1)directly without expanding
3(k+1)(k+2)

[sfundomsezane]

do you have a video for Division algorithm for integers

[XX-sfeh]

This is the first time that I've understood induction. Thanks a lot. 😃

[paul]

Your presentations and explanations are just stellar.
Thank you so much.

[mikethorner]

Thank you so much. I would always get mixed up with placement of the n and the k.

[emmanuelmusa-jh]

Thanks bro wakanyanya iwewe lm telling all my friends about you here in Zimbabwe @ Chinhoyi University of Technology....

[holyshit]

What about this case
Let T_{n}(x) = \choose 2m}\cdot{m \choose k} x^{n-2k}
moreover we know that our T_{n}(x) should satisfy following recurrence relation
T_{0}(x) = 1
T_{1}(x) = x
T_{n+1}(x)=2xT_{n}(x) - T_{n-1}(x), n>0
Can we prove that T_{n}(x) = \choose 2m}\cdot {m \choose k} x^{n-2k}
by mathematical induction and how it looks like

[WhatAmI-JB]

You make things so clear that any one cam understand.Thats what teaching is all about;ie to make others understand what you are talking about.
Not sll can do that.Thanks.

[jensberling]

Dr. Newton, I really appreciates all your works in mathematics on the, platform YouTube. It is so good to see your care for students by showing them your outstanding understanding of mathematics. Your clear thinking is an example to be inspired by in our lifelong learning.