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

[@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.

[@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!

[@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

[@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.

[@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!

[@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.

[@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

[@robertreynolds1849]

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

[@emmyb0y]

😶

[@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

[@RulvTeam]

Better than teachers, 10/10

[@mysteriousiamjewishmysteri2373]

RulvTeam how many teachers are better then that?

[@entitydoesvids]

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

[@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

[@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

[@AmericanScholar82]

Thank you so much! Your explanation was 100% better than my textbook, in which the author skipped several steps in completing the Inductive Step. Now I get it!

[@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.

[@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

[@yokaze_0014]

Dude genuinly nobody ever saved my life like this except at my birth. I finally understoof the Induction step i cant believe my brain didnt compute that we just needed to replace the Induction step with the Induction Hypothesis omgggg thank you!!!!

[@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!

[@matthewzaczeniuk4892]

You explained this topic in 7 minutes, something my professor couldn't explain in 2 hours! Thank you!

[@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 :)

[@dr.birendrakumar4649]

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

[@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!

[@yashkalyani5995]

when you released this video i was only 9 years old but today it was helpful for me after 11 years so thanku

[@DanniLKoss]

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

[@JStubblefield79391]

Every time I’ve seen an inductive proof example, I always thought the inductive step was illogical and failed to see the elegance of induction. This clarified all of that, thanks!

[@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.

[@sirlancerstien]

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

[@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)

[@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.

[@zaidofficials]

I deny to believe this gem is 11 yrs old

[@mickeywebb6850]

The only video on KZbin with a proper explanation.

[@Ralve_]

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

[@ignisninja5867]

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

[@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

[@wnnrmn]

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

[@Ohm_Sharma]

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!

[@marshmallow1553]

You saved me. I watched other videos and asked chat GPT, but you are the one who made me understand and solve different questions with your method. Thank you

[@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?

[@bestmovies3207]

11 years !! And it's still so helpful

[@felixad.9788]

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

[@yogaprakasam892]

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

[@ibraheemalmalki2555]

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

[@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!

[@Noahcom12]

This is where students go to 1day before exam ...

[@daimwasim635]

2 hours before😂

[@manya-w6]

​@@daimwasim635same😂

[@daimwasim635]

@@manya-w6 😂😂

[@collinslagat3460]

I have exam tomorrow 😅

[@petermusimbison6563]

Found these solutions so vital. Thanks a lot! Plz keep it up!

[@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?

[@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!

[@graciarivas871]

GOD BLESS YOU!

[@brainrotpookie]

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

[@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.

[@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

[@udehbonaventure222]

2024 anyone

[@Abhishekr1413]

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

[@anosvoldigod2943]

Holy cow this is 9years old😂

[@dhruvveersinghtanwar3336]

11

[@idrisrasak9445]

Now 11 years

[@onwukanjojohn3958]

Now 11

[@priyantm9120]

Still exist😌

[@PseudoTertiothrow]

Well I’m sure the actual proof is way older than this video. Is not like it will change

[@ethan6708]

This video was **chef's kiss**. Avoid TrevTutor and Kim Brehm for this topic. This video was 100x clearer

[@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.

[@nehafernandes2390]

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

[@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 !!

[@alberthmckenzie2772]

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

[@trusun3528]

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

[@RakibAhammed-lo2yr]

Because Our Earth People Only Need Certificate Result 😢😢..They Not judge your brain.

[@pinlivy9396]

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

[@justine4791]

this lesson fucks me up so bad

[@mimi_19]

Wow this is the best one yet

[@infowindow6932]

sir, you are good.

[@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.

[@eldes23]

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

[@jenniferaboujawdeh5978]

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

[@NehaYadav-qy6ok]

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

[@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.

[@water_wind_]

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

[@exolovesyouall3794]

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

[@napoleonbouchet9712]

You're not.

[@anuprasannan1310]

Nope..🤣🤣

[@bellsfiz]

I'm learning this in Japanese and I don't understand a thing my teacher said. You're my life saviour. I love you

[@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??

[@samuelbardi454]

Helping students even after 10yrs. That's what I call excellent teaching

[@moviescenestelugu4933]

Seeing before exam that's why we called legends 😂💙

[@BobSagetttt]

ThatTutorGuy goin hard on the ads...

[@ned7754]

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.

[@JackSparrow-Pirates_Caribbean]

Highly appreciated n respect for you from Pakistan

[@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.

[@sodiqtele4484]

This teaching is very explanatory, you are a very good tutor

[@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?

[@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

[@seemarajput8446]

U explain in simple method ............. It's easy.

[@bipultamang7061]

Been 7 months and didn't understand it and now in just under 7 min i understood everything thanks

[@sleepypanda7172]

KZbin is a blessing now a days

[@CyrllHeart]

Thank you so much, CS student here having a hard time

[@Noellexafael]

OMG i finally got it, my teacher never explained the thing that one side is equals de other so he just worked one side of the equation and said it was good and i never got why, thanks a million

[@shaddykioko9253]

The best explanation ever for mathematical induction concept

[@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!

[@danielavallejo5144]

Thanks this helped me a lot. Especially when my teacher wanted to give up on me because I didn’t understand it fast.

[@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!

[@ryangarritty9761]

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

[@sheridan.mp3]

Regardless of what I get on my final you've made this clearer than any video I've seen thus far. Thank you! (Wish me luck haha)

[@saswatighosh9177]

Whoever explained this ...thnx a lot coz just explaination of this single sum helped me to cover up the whole chapter in time...u r explaination was amazing...I would recommend everyone to be a part of this channel.... again thanks a lot....

[@lonemotheo1964]

Is this proof of equalities

[@saswatighosh9177]

@@lonemotheo1964 no....this is mathematical induction.... proof of equalities is different .( Mathematical induction is a chapter from class 11)

[@lonemotheo1964]

@@saswatighosh9177 so how does it work do I do induction before proof of equalities or I just do proof and forget about induction

[@saswatighosh9177]

@@lonemotheo1964 yup first do the mathematical induction

[@user-rj8tr6sp7e]

I just understood this in 7 minutes 32 seconds. Thanks so much!

[@aikaterina5331]

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

[@michaelkaliber]

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

[@zxcFlezys]

11 years old omg, tysm dude, my teacher didnt explain how to do and tommorow we have a test, all the people from my class didnt understood, but now i now its actually easy,💝

[@Andrink]

ALL the other explanations over-complicate this SO freaking much. I showed this to a friend of mine and she got it faster than after watching all the other videos :)