The induction step is not the assumption that something is true. The induction step has the form of an implication-IF the statement is true for k THEN it is true for k+1. That's why it's called a step.
Thank you so much for this. I've been beating my head against induction since I started caring about it (which was yesterday) and now I think I've got it. I wasn't getting the substitution of k^2 for everything left of the +1 term in the sequence, and now I am. I think you've helped clear a major block for me.
Fantastic tutorial, keep up the awesome work! I was struggling with this at my Uni lectures and test, but I'm finally starting to get the hang of it. Thanks for keeping it simple.
@@designtip7268 hahaha, I did manage to pass the course and got my degree. Been working as a software developer coding pharmacy software for the past 7 years. I wish you luck man!
This guy is amazing! I was so lost when my professor taught it to me and even more lost when I tried to read the textbook. I only had to watch one example and it clicked right away!
The other videos didn't help me at all. But this video was the same exact problem I was stuck on. So when he explained each step it was extremely helpful!
Still dont get it. I get lost when you state that 1+3+5+...+(2k-1) + *(2(k+1)-1)* = (K+1). I know i'm missing something but i really dont know where (2(k+1)-1) came from. I know how you derived (2(k+1)-1) i just didn't understand why you had to add it to 1+3+5+...+(2k-1) if 1+3+5+...+(2k-1) is n = k, then, n = k + 1 would be 1+3+5+...+(2k-1) *PLUS* some representation of 1 wouldn't it. A bit confused here
+k2datrack Greetings from NK. If the last term in a series is n, then the term before it is n-1. If the second to last term in a series is g, then the last one is g+1. The term before (2(k+1)-1) is (2k-1)
Since both side are equal P(1) holds true, then it wouldn't matter if n^2 was on the left and (2k-1) on the right, correct? As in if they were swap you can still work with the RHS, meaning it doesn't matter whether you're using the LHS or RHS to show P(k+1) is true when adding/replacing n with (k+1)?
Sir good morning tq u so much i have one doubt sir i lost my original certificate in home shifting and i have taken duplicate from board will it useful for my job sir replay me
good explanation; alot of people will skip the definitions in the beginning of the video.. i like how you explained it. it seems like others do not actually understand it but regardless they are unclear.
thank u soo much for explaining us in such abriliant way , you method and of teaching is very good , i like it ,you have cleared my concept about mathematics thanks again. A great love from PAKISTAN(the land of good hearted people).
Im confused on how your just allowed to assume that 1 + 3 + 5...(2n-1) = n^2 works for every integer how do you know the function doesn't break under a certain number ? Shouldn't this statement be a whole another proof to itself ? I've always liked math cause concepts can be traced down to there very core but this perplexes me cause how are you allowed to just assume a statement to be true. I understand how technically it works since you proved your base case to be true but I just feel like induction is a ghetto way of proving a function. I just feel like for every formula proofed by induction there is a better more conceptual way to proof it.
I saw your first video explaining Mathematical Proof by Induction and tried solving this problem by myself. Turns out I misinterpreted 'z 'for '2' in (zn-1) and laughed so hard at myself.
but if you plug 2 in the formula you'll find that the number 3 you get is not = to 2 squared. I don't get it. 3 is not = 4. I mean it obviously works for 1, but how could it work for any other number? EDIT i get it now, you obviously sum it with the previous term
That is exactly the point. If we can't test for some large sample, why can't they, and I mean none of them will use the the second number. Maybe there's something they all take for granted.
BEST math video on UA-cam about mathematical induction!
I didn't even skipped the ads just to help you :D Thank you for sharing your knowledge.
Cant stress enough on how much this video helped me through my first IB chapter!!
I watched a bunch of these, and just now got exactly what I am supposed to assume. Thank you so much for the clear explanation and handwriting.
you are welcome
Paul, thank you for this video. My "Night" just turned to "Day" with this Induction tutorial... Example was clear and very useful!!!
Thank you gents! In just 10 minutes you helped me understand this, which my professor failed to do in 150 minutes...
haha
Waaay better than my math teacher
Exactly!
Yep
I agree. Way better than our Computer Science Professor.
The best teacher
I had to go here because my professors speaks quickly and I can't read his handwriting lol. I get it! Thank you.
Hi Paul, may I know how do you write these question on computer? I mean how do you record on computer.
The induction step is not the assumption that something is true. The induction step has the form of an implication-IF the statement is true for k THEN it is true for k+1. That's why it's called a step.
This is awesome! Was struggling in induction, but this helped so much! Keep making videos!!
Zor zor gap yoq .l am uzbek .
Good vedio
6:44 literally what i needed
Thank you so much for this. I've been beating my head against induction since I started caring about it (which was yesterday) and now I think I've got it. I wasn't getting the substitution of k^2 for everything left of the +1 term in the sequence, and now I am. I think you've helped clear a major block for me.
Fantastic tutorial, keep up the awesome work! I was struggling with this at my Uni lectures and test, but I'm finally starting to get the hang of it. Thanks for keeping it simple.
yo where you at man you watched this video 9 years ago you still alive? am taking quiz tomorrow that why am watching it
@@designtip7268 hahaha, I did manage to pass the course and got my degree. Been working as a software developer coding pharmacy software for the past 7 years. I wish you luck man!
This guy is amazing! I was so lost when my professor taught it to me and even more lost when I tried to read the textbook. I only had to watch one example and it clicked right away!
Thank you so much! You explained it in a way that was very helpful! You saved my ass! Literally!!
thank you so much for explaining where the k+1 came from, I watched the khan academy video and I was so lost. you explained it so much better
Bless you and your videos
Wow, after spending so much time trying to figure this out after one course, your step-by-step explanation really broke this down for me. Thank you.
Thank you so much, To me it was the most understandable and detailed lesson on the Internet.
thank you so much for making these videos.
Thank you so much you make it easy
The other videos didn't help me at all. But this video was the same exact problem I was stuck on. So when he explained each step it was extremely helpful!
Thank youuu youre a life saver to my assignment jusq
I've read through my notes so many times and never got it! I then watched your videos and it clicked immediately!
Still dont get it. I get lost when you state that 1+3+5+...+(2k-1) + *(2(k+1)-1)* = (K+1). I know i'm missing something but i really dont know where (2(k+1)-1) came from.
I know how you derived (2(k+1)-1) i just didn't understand why you had to add it to 1+3+5+...+(2k-1)
if 1+3+5+...+(2k-1) is n = k,
then, n = k + 1 would be 1+3+5+...+(2k-1) *PLUS* some representation of 1 wouldn't it. A bit confused here
+k2datrack Greetings from NK. If the last term in a series is n, then the term before it is n-1. If the second to last term in a series is g, then the last one is g+1. The term before (2(k+1)-1) is (2k-1)
You legend!!! I actually understood this now thanks to you!
Thanks this is what I needed to understand this method
Since both side are equal P(1) holds true, then it wouldn't matter if n^2 was on the left and (2k-1) on the right, correct? As in if they were swap you can still work with the RHS, meaning it doesn't matter whether you're using the LHS or RHS to show P(k+1) is true when adding/replacing n with (k+1)?
2k-1 can't exactly be replaced as it is the maximum sum/the rule but you could probably multiple both sides by negative 1 if you would prefer.
This is the best video on proof by induction that I have seen. I’m sharing it with my 12 year old grandson.😊
Thank you! This is the best explanation Ive seen
Sir good morning tq u so much i have one doubt sir i lost my original certificate in home shifting and i have taken duplicate from board will it useful for my job sir replay me
Way^2 better than my Math lecturer!!!!😉😂
why is it 2k+1 + (2(k+1)-1) how does that carry over to other problems
I watched 5 videos about math induction so far and among all of them this is the only video i understood. thanks
good explanation; alot of people will skip the definitions in the beginning of the video.. i like how you explained it. it seems like others do not actually understand it but regardless they are unclear.
Nice work,,,,,,, simple and straight forward 😊😊
Thank you
In induction, are we only to proof?
this is very good . induction understood fully !!!
Thanks so.much I now understand induction it remains recursion
k^2 can any one answer this? What symbol that arrow up how to get that?
thank u soo much for explaining us in such abriliant way , you method and of teaching is very good , i like it ,you have cleared my concept about mathematics thanks again. A great love from PAKISTAN(the land of good hearted people).
For the basis, if you did n=2 it doesn't work. You will get 3 = 4, and that doesn't work. Can you explain to me how n=2 would work?
same question here
Amazing thanks 😊
Im confused on how your just allowed to assume that 1 + 3 + 5...(2n-1) = n^2 works for every integer how do you know the function doesn't break under a certain number ? Shouldn't this statement be a whole another proof to itself ? I've always liked math cause concepts can be traced down to there very core but this perplexes me cause how are you allowed to just assume a statement to be true. I understand how technically it works since you proved your base case to be true but I just feel like induction is a ghetto way of proving a function. I just feel like for every formula proofed by induction there is a better more conceptual way to proof it.
I saw your first video explaining Mathematical Proof by Induction and tried solving this problem by myself. Turns out I misinterpreted 'z 'for '2' in (zn-1) and laughed so hard at myself.
can this be done the exact same way with recurrence relations?
i feel like the most stupid person alive this is so confusing
I will pray to God for you, thank you
YOU ARE A GOD SEND. I'VE WATCHED 10+ VIDEOS ON THIS AND I DIDN'T UNDERSTAND ANYTHING UNTIL YOUR VIDEO. THANK YOU SOOOOOOOOOOOOO MUCH!!
but if you plug 2 in the formula you'll find that the number 3 you get is not = to 2 squared. I don't get it. 3 is not = 4. I mean it obviously works for 1, but how could it work for any other number? EDIT i get it now, you obviously sum it with the previous term
+Ozterkvlt You are confused.....
3+1 is equaled to 4
Its the sum of the numbers....
That is exactly the point. If we can't test for some large sample, why can't they, and I mean none of them will use the the second number. Maybe there's something they all take for granted.
Why do you add (2(k+1)-1) instead of replacing k with (k+1)? 6:53
can u plz prove it for the next element using n+1,instead of using k,i wanna see how does it works...
Thanks from Azerbaijan a lot 👍
The best mathematical induction video on UA-cam. Now let me try out my exercises.
very clear explanation of the reasoning behind mathematical induction. thanks.
You just earned a subscription brother
Superb Thanks a lot for the tutorial
If n is a positive integer then 1/1.3+1/2.3+1/3.4+...+1/n(n+1)=?
this helped so much went from not understanding to BAM understanding
Thanks so much I understand now:)
OMG!!! Hey sir, you taught is as simple as it is 🤓
you are awesome dude. TYVM before you came along this all seemed like magic to me lol
thank you soooo much, you helped me a lot 😃. I understand much better than my teacher.
You sir are a god! Understood them perfectly. Thanks a lot!!
You would make an amazing math teacher. Thank you very much
THANK YOU!!!
Make a vedio on question 7 plz....I really need it..
Best video I’ve came across for prof by induction
great helpfull vid thanks
This is *magic*. Thank you so much for this helpful video!
huge fan of his teaching skills. Thanks a lot for even explaining small steps that made it much easier to understand.
Finally the first person that makes sense in this subject
Thank you so much for making this video. It helped me so much.
Patrick JMT step down, we have a new teacher
You are the only person who has made me understand induction so far. Thank you for your in depth approach. I wish others would follow suit
I can finally understand it, thank you!
thanks you legend!
thank you! this was very helpfull!!!
wow! thank you so much.
nice explain thank you
gracias profe!
Thank you! I was so lost before this video.
this guy is gifted.
THIS HELPED A LOT ...BETTER THAN MY PROF
good explanations but just speaks to fast
Helpful!
The real question is "why?"
What program do you use?
When n=2
(2(2)-1)=3
2^2=4
How does this make sense?
Make sure you add all previous numbers.
wow, you have no idea how much this helped me :) keep making videos!
No kidding. It's like a cloud has been lifted from my mind.
so satisfying it
Much appreciated lesson
how do you prove when 1+3+5+7+...+ (2n-1)^2 =n^2
that cannot be proven if (2n-1)^2, it fails at the base case when we assume n = 1, it works for (2n -1) not squared.
Can u make more videos.....
goooood stuff right there...
👍