Proof by Mathematical Induction - How to do a Mathematical Induction Proof ( Example 2 )

[@tinanicole3597]

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.

[@w0nnafight]

you are welcome

[@jacquelinevaliente774]

BEST math video on KZbin about mathematical induction!

[@nicky3217]

Thank you gents! In just 10 minutes you helped me understand this, which my professor failed to do in 150 minutes...

[@barnabasbett8502]

haha

[@Julia-by6vz]

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!!

[@cugamer8862]

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.

[@courtneybourquin5899]

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!

[@fadhlanwasim]

I didn't even skipped the ads just to help you :D Thank you for sharing your knowledge.

[@thatWonKrnGuy]

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.

[@maxmuller2667]

Waaay better than my math teacher

[@nutzndboltz]

Exactly!

[@elijahsokoni7997]

Yep

[@Z9R.]

I agree. Way better than our Computer Science Professor.

[@jimwatkins1664]

This is the best video on proof by induction that I have seen. I’m sharing it with my 12 year old grandson.😊

[@elijahsokoni7997]

The best mathematical induction video on KZbin. Now let me try out my exercises.

[@piececontrolkyleshorts5297]

Cant stress enough on how much this video helped me through my first IB chapter!!

[@arthuraghamyan7274]

Thank you so much, To me it was the most understandable and detailed lesson on the Internet.

[@robertimmanuel577]

I watched 5 videos about math induction so far and among all of them this is the only video i understood. thanks

[@madzs803]

This is awesome! Was struggling in induction, but this helped so much! Keep making videos!!

[@Hioka123]

Paul, thank you for this video. My "Night" just turned to "Day" with this Induction tutorial... Example was clear and very useful!!!

[@Zorisx]

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

[@moff181]

I've read through my notes so many times and never got it! I then watched your videos and it clicked immediately!

[@stefanmarjanovic4768]

Finally the first person that makes sense in this subject

[@safiyayuldasheva1096]

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!

[@FroZenL1Qu1d]

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]

yo where you at man you watched this video 9 years ago you still alive? am taking quiz tomorrow that why am watching it

[@FroZenL1Qu1d]

@@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!

[@chome-zf9xv]

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

[@techguru7176]

Best video I’ve came across for prof by induction

[@adilakhtar8104]

huge fan of his teaching skills. Thanks a lot for even explaining small steps that made it much easier to understand.

[@saubikhan7419]

The best teacher

[@frazebean5117]

You legend!!! I actually understood this now thanks to you!

[@cosc1018]

Thank you! This is the best explanation Ive seen

[@LeahMwiba-fn1ky]

Nice work,,,,,,, simple and straight forward 😊😊

[@nanakwame1061]

Thanks this is what I needed to understand this method

[@tman7022]

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.

[@cybxtra]

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).

[@amirxonfaktuz9685]

Zor zor gap yoq .l am uzbek . Good vedio

[@moribellorie]

THIS HELPED A LOT ...BETTER THAN MY PROF

[@cahannovruzova2469]

Thanks from Azerbaijan a lot 👍

[@undergroundmusic7117]

this helped so much went from not understanding to BAM understanding

[@crystaloneill6802]

wow, you have no idea how much this helped me :) keep making videos!

[@mjamesw2]

No kidding. It's like a cloud has been lifted from my mind.

[@eilacorder1512]

Thank youuu youre a life saver to my assignment jusq

[@zuekut]

You sir are a god! Understood them perfectly. Thanks a lot!!

[@sebastiaankimman3925]

You would make an amazing math teacher. Thank you very much

[@NohidJohn]

OMG!!! Hey sir, you taught is as simple as it is 🤓

[@michaelmwila3406]

this is very good . induction understood fully !!!

[@sheilamaepulot5662]

thank you soooo much, you helped me a lot 😃. I understand much better than my teacher.

[@jamesrobertson9149]

very clear explanation of the reasoning behind mathematical induction. thanks.

[@shanaejarrett1043]

this guy is gifted.

[@moonlight_pixie8395]

This is *magic*. Thank you so much for this helpful video!

[@darrenmaverick]

6:44 literally what i needed

[@rachelkim9159]

thank you so much for making these videos.

[@CornKarama]

You just earned a subscription brother

[@MustCricket110]

Hi Paul, may I know how do you write these question on computer? I mean how do you record on computer.

[@eggfishy]

I had to go here because my professors speaks quickly and I can't read his handwriting lol. I get it! Thank you.

[@shawnajohn2610]

Thank you so much for making this video. It helped me so much.

[@Nikkeishajk]

you are awesome dude. TYVM before you came along this all seemed like magic to me lol

[@alexbarreto8774]

Thank you! I was so lost before this video.

[@behpable]

I can finally understand it, thank you!

[@YoungVinny]

Way^2 better than my Math lecturer!!!!😉😂

[@laibaaqureshi6228]

Superb Thanks a lot for the tutorial

[@erikpierce6241]

Patrick JMT step down, we have a new teacher

[@barbaramaldonado2195]

Thank you so much! You explained it in a way that was very helpful! You saved my ass! Literally!!

[@kurdistanhomeschool4471]

Amazing thanks 😊

[@hansypants]

Bless you and your videos

[@orangeleon7]

Why do you add (2(k+1)-1) instead of replacing k with (k+1)? 6:53

[@cellardoor70]

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.

[@Sophx16]

Thanks so much I understand now:)

[@reitchienishi6169]

Thank you so much you make it easy

[@ibadanmalik5084]

Thanks so.much I now understand induction it remains recursion

[@vasegt]

thank you! this was very helpfull!!!

[@marchanselthomas]

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.

[@MrTruman2cool]

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)?

[@ndzd07]

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.

[@SpacedudeGFX]

can this be done the exact same way with recurrence relations?

[@leoniduvarov6565]

Much appreciated lesson

[@TheFotoGuys]

What program do you use?

[@RoselineLopez-we3yp]

In induction, are we only to proof?

[@bellsb9426]

Where do we get K+1 from ?

[@learnmathtutorials]

Think about it this way. k is simply a representation of the n value that we choose. For example in the cases n=1, n=2, n=3, k is the 1, 2, and the 3. So k+1 really just represents the next case. If k is 1 then k+1 is 2. If k is 2 then k+1 is 3. If k is 3 then k+1 is 4. So really (k+1) is how we would write the word "next", but with math notation. Now if we think about it as the word "next" rather than (k+1) it all starts to make some sense. If n=1 is valid (our basis step) then the "next" (n=2) is valid. If n=2 is valid then the "next" (n=3) is valid. If n=3 is valid then the "next" (n=4) is valid. and so on... All the dominos fall down. Now we can see that this works for any integer 1 or greater of our choosing.

[@stranglesensei]

gracias profe!

[@pquic]

great helpfull vid thanks

[@rishikessharma9921]

Make a vedio on question 7 plz....I really need it..

[@sanahabib978]

wow you made it easy :)

[@kvislab]

how do you prove when 1+3+5+7+...+ (2n-1)^2 =n^2

[@richardrampersaud6818]

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.

[@jeremyr7320]

wow! thank you so much.

[@hlokomani]

thanks you legend!

[@sanchezregiemarkb.2916]

k^2 can any one answer this? What symbol that arrow up how to get that?

[@knowledgeboy6137]

nice explain thank you

[@ashkon7408]

why is it 2k+1 + (2(k+1)-1) how does that carry over to other problems

[@MariaPaula-fc3mh]

can u plz prove it for the next element using n+1,instead of using k,i wanna see how does it works...

[@alyaaalmadani9886]

I will pray to God for you, thank you

[@Bkaz3678]

THANK YOU!!!

[@Ozterkvlt]

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

[@KenrickM]

+Ozterkvlt You are confused..... 3+1 is equaled to 4 Its the sum of the numbers....

[@samueladler9080]

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.

[@care2goo]

goooood stuff right there...

[@MadhusmeliyMadhusmeliy]

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

[@gabrieladraganova5982]

thank you!

[@YG-up8by]

thank you so much.

[@himanshubhushan3927]

hi

[@lavanlaugh1574]

When n=2 (2(2)-1)=3 2^2=4 How does this make sense?

[@joelm2]

Make sure you add all previous numbers.

[@sannanhassankhan8281]

If n is a positive integer then 1/1.3+1/2.3+1/3.4+...+1/n(n+1)=?

[@cricketworld4849]

Helpful!

[@vivaldikonzsmith7291]

Thank you

[@mandevlol]

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?

[@danieldorsz1047]

same question here

[@usiqkeys7338]

Can u make more videos.....

[@k2datrack]

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

[@KimmyJongUn]

+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)

[@Mark-fy3fz]

But still I would love him to be my instructor instead😓

[@sebastiancolon8378]

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.