Proof by Mathematical Induction - How to do a Mathematical Induction Proof ( Example 1 )

In this tutorial I show how to do a proof by mathematical induction.
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[@EggheadWA]

If all math teachers were as clear and concise as you, math wouldn't be considered a hard class. Thank you so much!

[@bishwobhandari6002]

EggheadWA well said 👏👏

[@n.girlz7292]

yup 100% right

[@Barbarian_Queen]

Liking this comment after 6yrs 😝

[@danchuorabraham4424]

You've said it all 😂

[@mssttr]

bro was not concise

[@sanskaryadav2295]

You posted this video 10 years before and still, it's helping people. Hat's of to you man.🎉

[@enganewguinea]

True indeep bro. I am getting help from this video now - 2024.

[@AlmostAnything]

what if I say I spent fking hours to grasp this thing then finally i found this video. thank a world !!

[@ukashi694]

@William John Lol I doubt you understand anything happening in this video.

[@SAV1080p]

i totally get you man! i was think too hardly about it, when its as simple as this guys video. LMFAO

[@cr3qm650]

honestly same

[@adyfern]

same, i was about to cry out of frustration since I cant get step 3 and I've been trying to for more than an hour when I found this vid smh

[@89uchenna]

all I need to hear was 'replace'..you are a legend

[@hassankumail1053]

SAAMEEE!

[@ScrepisPrikolistas]

EXACTLY! I didn't understand that part as it was very unclearly put

[@abdullahasif7992]

Uchenna it was the same for me I spent 2 hours scratching my head but just this one word cleared it for me

[@20mymysf]

Me too!!! Like why didn't my teacher just say that simple word?!

[@daniellepeddie7427]

lmao

[@Dayz3O6]

Screw the text book your explanation is much better!

[@bharatsharma1026]

these text books seem to ruin it for us

[@petrosandfriends7315]

Dayz 3O6

[@AdonayZenebe]

Text book are either designed to filter out a lot of people by boredom or are just not compatible with much of the new generation.

[@mysteriousiamjewishmysteri2373]

Dayz 3O6 why is there so much knowledge ✖➗➕➖🎓to learn never keep pace?

[@BenMartic]

But you can't literally screw your text books for real

[@cosymarissa]

when you pay $200 for a uni textbook and a FREE youtube video explains it so much better and clearer...

[@mysteriousiamjewishmysteri2373]

MarissaMars why yes it does if one has mind heart stomach spine to think ?

[@narghile7594]

doesn't that just piss you off. high tuition fee's high textbook fee's and free ass youtube os the me teaching you shit.

[@BlueFluGaming]

Piracy is the key to success my friend. Never bought a single textbook XD

[@samermohamed7644]

This is why online PDFs exist

[@bekaluetsub1231]

Keep it up your clarification in this way .....

[@SciShorts]

This is where students go to when their teacher aren't good in explaining well.

[@mysteriousiamjewishmysteri2373]

Angelo Consunji how so say population of mutant humanity raises?

[@nymphalidae5873]

Yep im here after 3 hours of poor explainItions at uni

[@biancasatria4193]

It helped me a lot thanks!!

[@alfredox7741]

Exactly on Point :)

[@amitarani3973]

U r absolutely right

[@Ravishar-maa]

its 2019-2013= 6 years old video still useful! thnx from India

[@deepakshinde2288]

Yes thaks from India🇮🇳

[@ngd931]

I used induction and proved your equation right

[@matthewtrent1981]

@@ngd931 Came here to say this hahahaha

[@Eunanibus]

When a student finally understands something after some difficulty, it's utterly awesome to be able to tell a teacher thank you for their perfect way of teaching you. Thanks so much!

[@erikmachado4489]

This is the video I 100% recommend for anyone to watch. I watched so many other videos and did not understand it, but what really sets this video apart is him breaking down every step he is doing. And when it comes to proofs and discrete math one step is enough to make you completely lost. GREAT JOB!

[@lordmortymer]

This is probably the best video about proof by induction that I found. Very clear steps, unlike most that skip minor details. For those who are taking discrete math, I recommend you watch this video.

[@RulvTeam]

Better than teachers, 10/10

[@mysteriousiamjewishmysteri2373]

RulvTeam how many teachers are better then that?

[@entityflex]

@@mysteriousiamjewishmysteri2373 1% of the teachers on the planet, really not that much teachers.

[@robertreynolds1849]

Hi Paul, I am a mathematics teacher and I want to congratulate you on this absolutely superb explanation!!

[@emmyb0y]

😶

[@celestemondragon6976]

You have just lifted an entire weight of frustration off my shoulders! Thank you so much! My teacher hardly taught this kind of lesson and I asked everywhere and no one understood it! So thank you for clarification! :)

[@circutgumbo6778]

ITS BEEN 9 YEARS hope life is going well for you

[@Zeus-nh7mc]

Watching this after 10 years of it's release and still the best video on this topic, I've found on youtube so far.

[@thevegetableaddict4625]

I watched a lot of videos on this mathamatical induction process. I really didn't have time to sit here on my macbook for more than 30 min to hear a big long lecture- even though I could've probably understood this stuff from watching it, but you are the only KZbinr that I came across tonight that really helped me understand the concept behind this. I take an online pre-calc course with MyMathLab and it sucks. I understood Sigma notation and arithmetic notation easy from my text, but this stuff is foreign to me. Good job with this video.

[@channuangadi8506]

Why you mentioned *macbook* there

[@Boosterized]

I had a dream that one day I will use my computer to actually study. Today is the most productive shit I've done with the computer since I bought it. Anyways the instructions were very clear, thank you so much.

[@ramziadil8613]

I had taken discrete math and am learning algo right now. I never really understood this concept until I watched your video! This is so clear and concise! Thanks so much for you work!

[@veilofmayaa]

I cannot thank you enough for explaining this so clearly. Not missing or assuming that the student knows a particular step and just skipping to the next, for not making it cryptic but factoring or doing any additional step. Thank you very much. I finally understood how this works.

[@mmmmmmeghan]

Missed a class due to AP testing and stumbled upon this video while trying to catch up at home on my own time. Must say this is the most clear and concise math video I've seen, thank you so much for producing the content you do! Students everywhere appreciate it - staring blankly at the book trying to make sense of all these variables and integers just wasn't working :)

[@isatuk1682]

Thanks so much, this is the ONLY video that I actually understand. Even in class it just wasn't clicking, but this video really worked!

[@ichigo140]

I just want to say that this tutorial is amazing, and you sir have saved me tons of agony. I didn't understand this for a week, and you made it very easy to learn within 7 minutes. Thank you!

[@MrKushinator420]

My discrete math teacher is a first year PHD graduate teaching every problem out of the book, with the book's explanation. I could've just bought the book and gotten the same result, but You're like an actual teacher, thanks for existing.

[@ignisninja5867]

A perfect math example with clear English taught in an easy to understand way. This is a gem to find.

[@atomm7316]

clearly explained. well done! have test in 9 hours. i better get some sleep for Discrete mathematics.

[@shubhsingh1115]

Atom M Same here bud

[@Med0o0ocraft]

Same, except my test is in an hour.

[@heritageking]

me right now at this very moment

[@Pungiish]

Mine is in a week. I really need to pass.

[@davidpaultaylor93]

so did you get an A?

[@felixad.9788]

Wow, your explanation is really easy to understand. Thanks a lot!

[@sirlancerstien]

FINALLY, an explanation that actually explains every step instead of randomly having k show up with no explanation. Thank you magic math man!

[@kalenclayton]

I've watched a few Induction Proof videos and have left feeling just as confused as I did prior to watching. This one made so much more sense. Thank you!

[@kevinmontano3133]

Loved your explanation! Textbook didn't really make it clear that I could replace the left part of the induction step with the base case on the right

[@Ralve_]

Wow! This is so well explained, been struggling to understand this for like three days, not anymore!🙂

[@yogaprakasam892]

Seriously nobody explains it this much understandable.keep doing sir thank you so much 👏👏👏👏

[@ryangarritty9761]

This is by far the most lucid explanation of this proof I have found. Many thanks.

[@SpazzHobo]

Dude this is great. I am currently going through Apostol's Calculus and this helped me grasp the concept of induction real quick. Thank you so much. I appreciate you man!

[@ibraheemalmalki2555]

There was days when I hated studying these stuff for my university courses, Now after my employment I miss those days.

[@bestmovies3207]

11 years !! And it's still so helpful

[@gamaltk]

You're a legend. Straight to the, very clear ideas, well presented and organised. Thank you so much!

[@Twiistedmind]

So basicly, this was a very good video. I'm basicly trying to express my gratitude here, so basicly keep up the good work. (no pun intended)

[@lyricsmusics100]

this is amazing my professor gave us a take home test and this is the exact equation lol

[@pranayagarwal9372]

lyricsmusics100 lucky dude😂

[@gardenmenuuu]

What have you become now by job?

[@PhoenixRisingLoL]

5th source i am looking up - and you finally managed to explain it in a way i understood, as you actually showed the steps through. Thank you so much!

[@nehafernandes2390]

After watching multiple videos of same question, I finally understood the concept here 😭Thank you so much sir

[@graciarivas871]

GOD BLESS YOU!

[@trusun3528]

Why do I pay my school when I can just go on youtube and find a better teacher

[@meganannebrozek]

I've used this video for both my computational and discrete mathematics course. Thank you for the clear explanation!

[@alberthmckenzie2772]

Wow! My teacher preached his heart out over 2 whole class and I got this in 7 minutes. Thanks man.

[@justine4791]

this lesson fucks me up so bad

[@YeeJn]

I am watching this tutorial.. because my teacher just finished a 4 hour(!) class which I did not understand any of that shit. This tutorial just made it clear within 7:32.

[@water_wind_]

Thanks for posting the ONLY instruction on this that makes sense!!!! Everyone else covering this makes no sense!

[@infowindow6932]

sir, you are good.

[@vaibhavsingh-iw7qx]

at 5:54 - You could have taken (k+1) common on the L.H.S that makes it (k+1)(k + 2) Great Video tho !!

[@anniamatthews6803]

Thank you so much! Have been struggling for hours trying to understand and you were able to explain it in such an easy way

[@jenniferaboujawdeh5978]

i've watched no less than 8 videos about this and yours was the only one i could grasp properly.

[@mallorykroll]

At around 6:00, instead of expanding the binomials, would it also be okay to factor out k+1 from the left side?

[@kiputkustik]

Mallory K think the same thing

[@w1ndro1d]

Of course, that's the more efficient way.

[@dilipchakraborty5575]

Yeah I did da same thing

[@badjr0]

Yep. That's what I would've did.

[@anosvoldigod2943]

Holy cow this is 9years old😂

[@dhruvveersinghtanwar3336]

11

[@idrisrasak9445]

Now 11 years

[@onwukanjojohn3958]

Now 11

[@priyantm9120]

Still exist😌

[@fpernice518]

Excellent explanation! I needed this for my graph theory class. Though it's somewhat unrelated to this tutorial, my textbook assumes that we know proofs by induction already. So I really needed a good explanation on how they work, related to graph theory or not. You nailed it, thanks!

[@mickeywebb6850]

The only video on KZbin with a proper explanation.

[@eldes23]

where's the part 2 ? is there? i wanted to learn more!

[@NehaYadav-qy6ok]

Thank you sir.... I was cofused in the k+1 th step of induction but u made it all right✔✔✔ ⬇⬇⤵⏬⤵⬇⏬⤵

[@peachyx2187]

10 years ago and this is still such a useful video, learnt induction just from this one youtube video faster than I learnt from my lecturer in a one hour lecture

[@johnpatrickgonzales5693]

Thank you for making it crisp and clear!

[@exolovesyouall3794]

am I the only one who see his reflection? ✌😂

[@napoleonbouchet9712]

You're not.

[@anuprasannan1310]

Nope..🤣🤣

[@BobSagetttt]

ThatTutorGuy goin hard on the ads...

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i know aye

[@thevegetableaddict4625]

Yep. They really do some heavy advertising. Google's search engine on youtube is great. I don't need to pay to look at videos that are free on youtube.

[@aishwarya6123]

I learnt more in this 7 minute video that I could ever in my 2 hour math class. Just Amazing!

[@marbiengregory5976]

Amazing! The exact assignment we had with our teacher in Masteral! Thank you.

[@kv8938]

I don’t understand. How does one example(basecase) allow us to assume for n= k. How is this a proof if the whole thing is based on an assumption made from one example?

[@dipstick1754]

This is my exact problem with this proof, and it drives me crazy. The only logical thing i can think of is that why wouldn't it be. Because nothing unnatural going to happen, like we get a complex number or something like that. But this is not a proof it`s just an assumption. Because of that reason i can`t call this a proof.

[@akkari16]

You dont need to expand k(k+1) + 2(k+1) ... {{(K+1) is common, just factorise (k+1) }}..

[@bettingshorts3764]

akkari16 nAiled it

[@rosienneyvettebataller2942]

akkari16 then how about the k qnd the 2??

[@leoniduvarov6565]

Thank you so much! My professor and other you tubers tried, but you really made this so clear and easy to understand. Keep it up

[@chiararoyale5183]

I've watched about 50 videos on this topic and this is the only one that actually helped

[@ryanr4156]

You missed a step at the end. You have to write out the "therefore" statement at the end that shows you are making the conclusion "Therefore 1+2+3+...+n+n(n+1)/2 for n>0"

[@j.kaimori3848]

Every school has its own rules there, it's the maths process and logic of it that most people get stuck on.

[@carcinogenicthalidomide3057]

Mathematical induction just might be the most useless chapter except for proving most equations.

[@PLazz257]

As a comp sci major, I cannot agree more that this chapter is so useless within the component of discrete math

[@randomperson9282]

JmethenDour // Ayeee same

[@sashamuller9743]

for an engineer it's not useless though :)

[@dragonvarine7553]

​@@sashamuller9743 What do you use induction for in engineering?

[@j.f.4859]

@Sasha Muller Same question. What do you use induction for in engineering? I cannot fathom why we are learning this. And frankly, it doesn't look like a very full proof way to prove something. I guess maybe to validate relationships after testing. Is this why?

[@cabbabbages]

This induction business was driving me insane, i just couldn't grasp it but you made it nice and clear. Thankyou so much!!!

[@MoDiscovery]

Looking back at this before my exam. It really gives me confidence that I can solve this duing exam. It is so simple, yet so detailed. It helps understand what really is going on.

[@canadianthroneholder]

at 5:55 you could go straight to factoring because (k+1) is a common factor of both k(k+1) and 2(k+1)

[@mb23ism]

It does not clearly follow that Showing: n = k + 1, follows from the basis of the previous long concatenated and previous assumption. You completely lost me there. There needs to be a "because" there somewhere, which is not to impose causality onto the math, but to bring explanatory coherence to bear upon that transition.

[@PaulProgramming]

Ok, how about this... We prove it for the basis n = 1. Then we say okay, lets just say we want to test it for n = 2. So if we say okay, lets let k = 1 then we can say that 2 = k + 1 because 2 is one more than k. If we can prove that k+1 works based on k working then we have proven that 2 works because we have already proven that 1 works in the basis. Then since we have proved that each k+1 works for every k that works, we can prove 2 works based off of 1 working, we can say that 3 works based of of 2 working, we can say that 4 works based off of 3 working, and down fall all the dominos. Hope that helps.

[@redrounin1440]

or think of it like this. Step one: show that it's true for some case. Step two: Assuming it's true for some case, show it's true for the next case. (really what you're doing is showing that the statement 'if one case is true, and by assuming one case is true then the next case is true' is true)

[@BillionDollarDealer]

Paul Programming You have a new subscriber ;-)

[@Basaltq]

Paul Programming and @@redrounin1440 thanks for the explanations! That cleared it up.

[@bridgetbouska3282]

Your explanation of proof by mathematical induction is very helpful. I appreciated the background information you gave at the beginning. The visuals were clear and effective. One element I would like to see in this tutorial is a bit more information on what inductions is and why it works to prove statements. In addition to that, it would be helpful to know what types of statements are best proved by induction. I admired the way you explicitly explained each step as you proceeded through the example proof. I liked how you showed a precise way of writing a formal proof. Thank you for the helpful tutorial!

[@gabbystillman6563]

thank you for making me the happiest discrete math student in the world :) i get it now!

[@castlewinds5422]

Wonderful video. Was actually confused with book steps now it is automatically clear through your example itself. Thank you.

[@sarahpl2713]

Thank you so much , this is the best video so far about Induction, very clear and easy to understand!

[@wnnrmn]

I'm gonna stop going for lectures so that I could focus on you, this is way more better than i was taught.

[@tejashchauhan579]

Such a good explanation!!😀 I have understood it finally today after spunning out 2 months. THANKYOU SO MUCH!!🤗🙌

[@craig7878]

In the top 2 best videos i've seen for math induction principle!

[@AndrewThacker]

This makes it so obvious where I was otherwise confused. Thank you so much.

[@happiguruman]

Amazing video. After a long time of solving questions using mathematical induction, it became difficult for me to get it again but your explanation makes it very simple and I am ready to go again. Thank you

[@DanniLKoss]

Aboslute madman, missed 3 weeks of school cus of cancer and you're a savior.

[@pinlivy9396]

You deserve distinction!!!!!!! May God bless you abundantly.

[@michaelkaliber]

This was the dumbed down explanation I needed. Thanks I really needed this...

[@jmckey]

WAY better explained than what's in the FTCE Mathematics 6-12 study guide (for Florida teacher certification exam). Thanks!

[@shanklen197]

15 min before I have to go take my first precalc exam. I was having trouble with the last step, and your video saved me when you said that Sk from the second step could be used for the third step!

[@akingbadeomosebi1495]

Just when i thought i had given up on this topic, i got the grace to search out once more and find your video as a reference from examfear channel, I study in India, but I'm not an indian, and the communication accent is quite a barrier, their terminologies (words used) aren't universal that everyone can understand, they sometimes speak in their native and i get lost, i've met 8 people to explain this for me over and over, they must have think I'm a dunce or dummy, but I just watched your video One time, and I was like wtf?... so easy..? is that all?.. Man I'm so grateful, Thank you for uploading such, it's a honor to learn it from you.

[@rman5001]

I stared at the notes my teacher gave me for an hour and couldn't figure this out. It took you 7 minutes to teach me and now I get it!

[@nmarriotti]

Great video! It helped me with a problem I've been struggling with for hours.

[@aikaterina5331]

i hope there are many of you out there T^T thank you for this T^T You are so good on explaining .

[@Serenity.Solstice]

I have a great prof, but I was having a hard time understanding the induction step the way she was explaining it. Thanks for using a less traditional method, it was really helpful!

[@HarriMehtala]

The best explanation so far, thank you!

[@WillSk8ForFood313]

You are AMAZING! I finally got it with your explanation... Thanks a ton!

[@gabzmann7270]

This is the best mathematical induction video.Thanks so much!

[@abhishekr5104]

Man...... You are the best...... This is like the best maths class i have ever listened

[@tizah96]

THANK YOU SIRRR! You are the best. Clearly explained!

[@robertgarner2036]

This is a brilliant video for understanding induction! Thanks!

[@dr.birendrakumar4649]

My day became excellent after seeing this!! Helped me!!

[@laloortiz3499]

THANK YOU SO MUCH MY TEACH DIDNT EVEN EXPLAIN THIS. I HEART THIS CHANNEL