Induction Inequality Proof Example 4: n! greater than n²

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Eddie Woo

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Why this guy have his thermostat to the left of his math homework LMAOOO thanks for the help though

Lempy

A good teacher need good comment.... your explanation was excellent
Thanku for sharing.

punamgupta

Thanks so much for your time in proving this! It was a huge help!

emilys

Thanks Eddie for really teaching me and simplifying the maths.

Bouloune

I think it should be valid for every positive number greater than or equal to n, not only positive integers as Eddie mentioned.

tahatariq

Thanks a lot sir! I got my respect back through this sum!🤗🙏

kcx

Can you please cover strong induction?
I have a test after xmas, and I already get weak - it is the difference that confuses me. Many thanks

Paddys

wow that technique at 5:50 for completing the square like that to manipulate the problem further is beautiful.
I've always wondered if perfect squares could be done with fractions, but in the practice sets that question never came up.

tauceti

My "increasing gap" trick works again to greatly simplify this proof:
(n+1)!-n!>(n+1)²-n²
n!*(n+1)-n!>n²+2n+1²-n²
n!*n>2n+1
Now it's clearly visible, but just to do it a bit more proper, let's divide by n (which works, n>0):
n!>2+1/n
And 2+1/n<3 for all n>1, so n!>3, which is definitely true for n>4.

Can we still send math problems? I'm having trouble with this problem:

Prove by induction that
3^n < n!
when n is an integer and n ≥ 7.

SaintAntRox

Is there a faster way we can do this problem? This explanation seems unnecessarily long.

Shingorani

Hi Eddie
You are doing great. I have a question which is
"n factorial >=2^n-1"
Please do solve this

AliHassan-zyqt

Hi Eddie! Your videos have been a great help for me and I would be very greatful if you could answer my question as well.

Why can't I just rewrite (k+1)k^2 -(k+1)^2 to k^3-2k-1, and put 4 instead of k ? I would then get 55 which is positive! Is it because I then would need to prove that k^3-2k-1 is positive for all numbers above 4 as well, which in turn would need its own induction proof?

Gaaraape

3:53 - Where did that k in the 3rd column come from please? It looks like you just added a random number (k) and attached it to the first number on the righthand side?...

evelynwallace

Why getting on his case about video length? is your ADD kicking in? I like his explanations, as a discrete math class student in a grad school class with no real math background, he does a better job than my professor and certainly better than the textbook.

tombranson