[Discrete Mathematics] Mathematical Induction Examples

In this video we discuss inductions with mathematical induction using divisibility, and then showing that 2^n is less than n!

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[BUILDUPMERCHANT]

mathematical induction is so confusing that sometimes you might not even realize you've got the answer😭

[jadchaar]

please do strong induction it is a lot harder :(

[Submersed]

I HAVE BEEN LOOKING FOR VIDS ON THIS FOR SO LONGGGG

[ryguyo]

Well If I could just do this for my proofs it would be awesome, but my professor needs more than this. So thanks for the shortcuts!

[gordonchan]

can be proven by cases too:
case 1: n=3k
case 2: n=3k+1
case 3: n=3k+2

[ianawilsonn]

Great video. Can anyone explain why n=(k+1) was used during the inductive hypothesis?

[Vertek]

where'd he get 2^(k+1) to be equivalent to 2^k * 2? I'm so confused on that part. Can someone enlighten me

EDIT: figured it out myself, so they're equivalent because for example 2^4 = 16 & 2^3 *2 = 16, 16 = 16 checks out

[celebritiestrend]

Pls could you solve for the sum of an AP sn =n/2(2a +(n-1)d)

[snowa]

At 5:20, I still don't understand why you added a 2 on the left side and a k+1 on the right side. Can someone explain? Thanks!

[kaziox]

How do I prove that 2^n>n^2, for every n that belongs to N and n>=5?

[ranger]

could someone explain to me how k! (k+1) = (k+1)! ?

[mayurkarmakar]

I have a question.Help me in solving the below question:

Q: Prove that 5^n-1 is divisible by 4. //(n is the power of 5)

[shanolinnaidoo]

This reminds me of hacking...where you have to use every piece of available information to coerce the outcome. I'm still shaky on this, but slowly getting there...

[jianma]

Wait in 4.48. 4! = 24? should be 10 ? ????