lol i can truly say this is a coincidence: the reason why i started watching your videos was because i was struggling with this EXACT inequality which was assigned for my homework! Thank you very much for your help!
I think you have a mistake at 6:29, when you expand the fractions. Shouldn't it be 2 - 1/c + 1/(c+1)^2 = 2 + (-1)/c + 1/(c+1)^2 = 2 + ((-(c+1)^2) + c)/(c(c+1)^2) = 2 - ((c+1)^2 - c)/(c(c+1)^2) ?
Induction Inequality Proof Example 1: Σ(k = 1 to n) 1/k² ≤ 2 - 1/n At time 5:44, how did you conjure up 2- (1/c+1) ? I mean, why do we have to specifically put it in that form? And how did you derive that expression?
***** Ah okay, I get it. I just wanna say, thanks for posting these videos. It helped me tremendously. I'm an undergrad in Comp Science and Discrete Math is such a torture.
Nice induction proof. Not a very strong inequality since we know summation(n=1 to infinity) 1/n^2 is famously equal to PI^2/6 = 1.64. compare to n=30 where 2-1/30 = 59/30 greater than PI^2/6
For those saying this proof is incorrect, change the sign of c at 6:26 and work the proof out. The numerator will be c^2 + 2c + 1 - c which simplifies to c^2 + c + 1 = c(c+1) + 1. If you continue with the steps after you will get the same answer.
lol i can truly say this is a coincidence: the reason why i started watching your videos was because i was struggling with this EXACT inequality which was assigned for my homework! Thank you very much for your help!
Aajtac nuse
.
I think you have a mistake at 6:29, when you expand the fractions. Shouldn't it be 2 - 1/c + 1/(c+1)^2 = 2 + (-1)/c + 1/(c+1)^2 = 2 + ((-(c+1)^2) + c)/(c(c+1)^2) = 2 - ((c+1)^2 - c)/(c(c+1)^2) ?
Yeah, there is a mistake with the signs that he took. My answer and yours match , but the video is still good none the less...
I wasn't really able to do this by using (c+1)² - c instead of (c+1)² + c at 6:30 . Just changes the solution .
At around 8:31 why are the terms subtracted instead?
All you did was split the fraction up, so why does it have to be subtracted?
***** Ahhh I see
Thanks Mr. Woo
How you make a + to - in this question can you please explain.
Induction Inequality Proof Example 1: Σ(k = 1 to n) 1/k² ≤ 2 - 1/n
At time 5:44, how did you conjure up 2- (1/c+1) ? I mean, why do we have to specifically put it in that form? And how did you derive that expression?
***** Ah okay, I get it. I just wanna say, thanks for posting these videos. It helped me tremendously. I'm an undergrad in Comp Science and Discrete Math is such a torture.
This is the best lesson for induction I've seen even though it is just about a single example
6:28 is wrong with the signs
he's correct. he did not multiply the signs as he's just working on the fraction independently.
Why did you change the positive sign to negative sign ?? I think that is wrong !
The negative (from subtracting) has to apply all parts of the fraction. It is correct.
@@crawfordcarson134 Thank u so much, I was thinking that quarentine was blowing up my mind
At 8:43 , why did you change the fractions to subtraction instead of addition?
Mistake with the sign at 6:29!! All wrong
06:23, error, must be 2-\frac{(c+1)^2-c}{c(c+1)^2)}
Sorry but why its minus? when you change it from a plus to a minus you have to change < to > and than its wrong
Fynn X si
Fynn X si
the only good explanation there is for this type of inductions
I love you
Nice induction proof. Not a very strong inequality since we know summation(n=1 to infinity) 1/n^2 is famously equal to PI^2/6 = 1.64. compare to n=30 where 2-1/30 = 59/30 greater than PI^2/6
Jesus Christ this man just saved my life
if c is negative, it still works.
I am stuck in a question of similar nature, could you please work it out for me..
1/1^1/2 + 1/2^1/2+...+ 1/n^1/2 > or equal to (n+1)^1/2
prove that if x and y are natural numbers such that k=(x^2 +y^2)/xy is an integer, then k=2
Not going to use induction.
x²/xy +y²/xy=k
x/y + y/x =k
x|y and y|x only possible when x=y(for integers). Plug this in.
x/x +y/y = k
1+1=k
k=2😄
@@TechToppers Hahah... Thanks. But you are 4 years late bro.
This is really complicated! You can use a telescoping sum: Sum(k=1,n) 1/k^2
Thank you!! The algebra was so mind bending on this one. I gave up after a while. Thank you for the video!
Never give up! That's all.
It feels unreal, but *Never give up* !
Bro, its 10 PM and i need to send my activity at 11 PM and i get stuck on this fucking question. You are amazing men. Thanks men.
In the 'Assume true for n=c' line, isn't it already given that c must be a positive integer, since c can only take the numbers that n can take?
Thanks for the help! Better than my professor for sure!
Prove that for all k ≤ n, pk(n) ≤ (n − k + 1)^k−1. Please someone solve it
thanks Yawei Hu
I like it second last line 3
thank u very much for making this vidd
Thank you for the wonderful explanation ! :)
Hii
Thank you, this was very helpful.
Thank you for your proof! I am trying to help one of my family members to understand proof by induction. Your method was easy to follow. Thanks again!
by the way thanks ....
because of you I am clear with induction
i want the proof of:
1/2^2+1/3^2+1/4^2+...+1/n^2
I've another cool method without induction. Wanna know that instead??
there is a symbol for positive integer: N
solve it again, it's wrong
my hero :)
Thank you ❤
For those saying this proof is incorrect, change the sign of c at 6:26 and work the proof out. The numerator will be c^2 + 2c + 1 - c which simplifies to c^2 + c + 1 = c(c+1) + 1. If you continue with the steps after you will get the same answer.
This is beautiful
ahhhhhhh founded 1st mistake in your video dude .....
jzt a small sign difference make that sum wholly different ......
very nice explanation
Thank you so much! Really easy to follow :)
6:29 wrong
This is beatiful!
Thank YOU!
Thank you very much for the video, you saved my ass big time..