❖ Proof by Induction ❖

[@CleverProgrammer]

I watched multiple other videos, read other textbooks, listened to professors, read blogs, listened to a podcast, and tried some other mediums of learning as well to understand how inductions work. This video was the best of all and ONLY one to help me get it, bar none. Thank you.

[@patrickjmt]

you are very welcome. come back any time!

[@P3R3ZC1D]

Thank you! Clear and concise explanation.

[@LifeWithYourMum]

... Listened to podcasts?

[@CleverProgrammer]

pr0duct lol yes.

[@Darkness-rs9sp]

Yes! same here.

[@bobba515]

Whenever I don't get something, I can these days guarantee that Patrick will make me get it. Wow.

[@patrickjmt]

:)

[@delalias5754]

i was thinking about spongebob for a minute

[@gandalfthecreator]

sace topic 1 year 12??? anyone

[@adrift2280]

@@patrickjmt the GOAT🙏

[@rosemarypatronellamatura4689]

i never understood induction forv the pst two years in advanced level and i avoided those questions at all cost .unfortunately wen i came to university i met INDUCTION but 1 hr on youtube with you changed everything.that was great.i like proving by induction now .thank you keep it up

[@samsaghafi4876]

You have literally taught me in 6 min what I have spent up to 10 hours learning from my professor, textbook, quizzes, and assignments. You r the best KZbin tutor. Thank you

[@swaysway5998]

I'm in tears because I literally was clueless when my teacher was teaching and this video is perfect. You have a gift, a rare talent of teaching. Thank you from the bottom of my heart. My anxiety has diminished for my exam tomorrow. THANK YOU

[@PersuasionBlasian]

You sir have taught me in less than 10 minutes how to do something we've spent hours in class time on. Thank you!

[@lovehearts1998]

Learned this in high school: didn't get it Learned this in college summer class: didn't get it Learned it in normal college semester: didn't get it Stumbles upon a 6-minute KZbin video: GETS IT.

[@FatBellyChemist1234]

I'm doing my maths exam revision and watching this makes me think why did I hate induction.

[@Jared-kh3uk]

Joelynn Carter I thought even prestigious high schools cap out at Lin alg or Difeqs

[@georgemendez6760]

@@Jared-kh3uk this is taught in both linear algebra and differential equations (to some extent)

[@Thechosenone1718]

@@texasrox2010 This is taught in UK schools. It's part of the a level further maths curriculum.

[@II_xD_II]

@@texasrox2010 in India its a part of high school syllabus

[@coffeeagent1]

From 8th grade all the way up to my senior year in college I still come to Patrick to for math help. Thank you for helping pass all these year my friend

[@patrickjmt]

you are so very welcome :) thanks for sharing the comment, that makes me feel good :)

[@stephenmack2160]

Your videos on induction, partial fraction decomposition, and derivatives are saving my life before finals rn tysm

[@MrMeagain569]

Patrick, you got me through Calc 1-3 and Differential Equations, and now you're coming through in Discrete the day before my exam. Can't thank you enough!

[@israelfailin4803]

Alright, I get proof by induction now, thank you. Guys, is there anything more painful than reading a discrete math textbook?

[@militantpacifist4087]

Israel Failin Reading and trying to understand a theoretical math textbook, like abstract algebra.

[@israelfailin4803]

Militant Pacifist Pretty much the same thing (don't get all math nazi on me now)

[@omarnsimpson908]

Sitting through a four hour discrete math lecture where the professor can't teach and just reads out of a discrete math textbook so you have to teach yourself by reading through the same part of the same discrete math textbook all over again. Yes, this is a true story. There is a Hell and that is it. QED.

[@Distress.]

Omarn Simpson I'm taking it online with a useless book that gives no more info than the professors bare bones ppt.

[@ismailniyaz5167]

Screw that, my professor gave me a discrete math textbook and I've gone through absolute AGONY over the past couple of months. Learning via videos like these, then attempting problem sets is infinitely better.

[@jaehyukoh3394]

As a current college math tutor, I think patrickJMT is the best KZbin math tutor. His explanations are x100 better than my professors.

[@Kurogames]

Oh god, I can't thank you enough for this bro. I've been trying to understand how to do this for almost a couple of months now, and nothing ever worked. The material provided by the teacher was confusing, the written material online confused me even further, but this, this just clicked. Thanks a lot.

[@konflictification]

Seriously though. Thank you so much. My professor's 2 hours lecture had me stressing as I didn't understand what the goal even was. I love the feeling of "ohhh, I understand what I'm doing." And you have provided me with that. Thanks.

[@patrickjmt]

my pleasure :)

[@slsinflorida]

Thank you from the future! I didn't understand the professor's lecture, didn't understand the textbook, didn't understand the first 3 videos I watched, but now I finally see where all of the "random" numbers that they where putting in came from. I really like that you didn't just assume we'd already know the concepts needed to do the math in this.

[@Richmanholla]

Dude you're the man. Clear and concise. I always come here to get quick and easy help. I've become codependent lol. Taking math analysis and the teacher was not engaging or clear, which happens at higher levels of math. Not sure if you take request but that'd be nice if you did. Nonetheless, I'm extremely grateful. Keep up the great work.

[@kurchak]

By the way, my university's official course content links to this video in its "Proof Techniques" lesson. And it's an ABET accredited Computer Science course (Algorithms and Analysis). And I don't mean like the professor said "hey check out this video", no, it's actually in the official published material lol. And they link to you! I think that is something to be proud of.

[@TakeItEasyC6]

You sir are the reason I should be able to pass my Discrete Mathematics final tomorrow. Thank you so much! Very clear, good speed, easy to follow. Keep up the great work!

[@demirsjourney]

did you pass?

[@ViaVanille]

Thank you Math GODS!! I have been having trouble understanding this and Thank Goodness that you have a video explaining it! Thanks Patrick! Im so happy I came across this because you are the only one I can understand math from on these YT vids and the only one that I enjoy watching and learning from.

[@TheMet306]

I did not learn this in 2 whole classes with my college professor but I learned it in 6 minutes with this KZbin video. I'm not sure if he's a terrible professor or if you're a great content maker, still, thanks for helping me not fail the homework.

[@TheIdontwannadothis]

I have been trying for hours and hours to understand induction, i watch your video and understand in 6 minutes, 29 seconds how to use induction. You are incredible, you are 100000 times better than the TA's at my university. Thank you so much.

[@BoomerFTW]

Thanks man, using your teaching for not only Calculus 2 now, but also my discrete structures class (CS 250), you are the best!!!

[@callofduty3man2009]

Have yet to meet a good teacher like Patrick and he didn't go to school for it like da rest of my professors did. Ur awesome

[@YoItsAero]

I see why pat is so good at math, because his left-handedness/right hemisphere power gives him creative ways to solve problems. thats a math professor right there.

[@VivisDoomsday]

Thank you so much patrick! Something I've been struggling with in class to understand clearly by my professor, and just watching your example once I finally understand how to prove this!

[@barbie7913]

Thank you for your clear explanation. I do not really have a problem with mathematical induction . The only problem I had was showing proof on the one side. But after watching your video,I now know.

[@EriksonAndStuff]

You helped me in AP Calculus, and now you help me in Discrete Math. You are my savior man.

[@jojo23srb]

Patrick JMT; the hero I need, not the one I deserve

[@danamuise4117]

You helped me get through pre-calculus with this video years ago. Now I'm in discrete math, learning proofs, and here I am, back again!

[@4345ghee]

Thanks so much PatrickJMT!! I really did well in Cal I,II,III, Linear algebra, and now discrete math because of your help! Much appreciated, and thanks for everything!!!

[@HeavensHeros12]

This has been the hardest topic for me in Discrete Math. I read my textbook and watched multiple videos; yours was the one that finally made it click. Thanks!!

[@SoiledShip]

THANK YOU! It's like my prof an TA think their teaching a bunch of prodigies in class and are teaching us with difficult and ambiguous problems. And you did it step by step an not assuming we knew what was going on. You're awesome!

[@VadelGame]

I spent a lot of time last night watching videos! you saved me back then on pre-calc, Calc1, but I didn't know you had discrete math material. Now I understand the steps of induction. Thank you!!!

[@siyethembasimlindile8382]

whenever im searching a topic on maths i include Patrick at the end just for em to take me straight to ya, ya are the best. thank ya

[@patrickjmt]

thanks! :)

[@jenniferfoust1193]

Yes!! Your videos helped me through my calculus classes, and now discrete mathematics. Thank you so much for all of your work. You help us all so much. All of my classes have been online, so the extra examples and thourough explanations are so good!

[@Bladex871]

Been struggling so long and this vid taught me in literally 5 minutes, great vid, best teacher i never had

[@ibraheemalmalki2555]

Already 9 years since I found your videos to study for my courses, I hated those times then but now I miss them.

[@iamthedarklord1314]

All i can say thanks a lot man. Your teaching method is clear and concise.

[@DrFirecapePhD]

They honestly need more teachers like you. you explain everything my teachers explain much faster and a million times more clearly. Thanks for the help

[@gugusloth]

Your hand writing is so consistent and I love how you're so concise!!!! Thanks for all the help :)

[@robertsevo7670]

comp sci too? Youre a champ, thanks for getting me through university

[@JadeMarena]

Thank you sooo much for posting these videos! I cant tell you how much i appreciate them and rely on them now. You make things so much simpler to understand and it really helps me get things right. Keep posting them! God bless you sir!

[@stevenan93]

cant believe i sat through an hour of lecture to end up learning the entire concept in 6 minutes! Its like second nature now thanks Patrick!

[@utku416]

I failed because of this stupid ass induction in my final exam, now I'm preparing for the makeup and thanks to you, I understood the subject perfectly. Good job Patrick, keep up the amazing work!

[@heteshpal96]

Awesome video I have been struggling on proof by induction for some time, my teachers decided not to help and said that i should try working it out. watched your video once and I understood it first time which is amazing. I really appreciate it thanks!!! :D

[@kameryn101]

math makes me want to die. Your explanations make me want to die less. thanks lol

[@patrickjmt]

: ) glad i was ale to help. there are quite a few more proof by induction examples by me if you need to see them (or practice yourself!)

[@Darknavy42]

Exam is in 30 minutes and yet again, I learn more from you. Cheers

[@leylaharoon6798]

thank you for helping me understand math all the time😁you are basically my teacher

[@du4l1ty]

Thank you Patrick! Your quick very clean notes helped me understand this almost instantly!

[@jenoharu]

thank you for all your videos 😭 you've been saving me since my calculus days 💖

[@oakvich]

Thanks for your videos. I like how you use more complicated numbers and equations in your examples. It really helps in understanding!

[@AayushBartaula]

watched it 10 years after this video got published thanks so much

[@underdogu2971]

wow! BIG thanks from Philippines! You're a great teacher. you only used 6mins to teach us this topic while my professor consumed an hour!

[@TodayinJensSewingRoom]

Amazingly helpful. Instead of staring blankly at my professor, now I get it! Thank you so much!

[@shaunohbi]

Man thanks so much for this. Not even both of my math teachers were able to explain this properly, I should be fine in my exam for this now (:

[@earnamasters]

I am a huge fan of all your videos, and not just when I have an upcoming exam!

[@aguilanthony]

This was so much simpler than the method that was presented by my teacher. He's an amazing teacher, but he dropped the ball on this one.

[@rajeevmasilamony7008]

I know you probably get this a lot, but you're a lifesaver. Thank you so much for making these videos, you've saved my grades more times than I can count.

[@RONANAWAY]

Used this back in 2017 for highschool calculus, returned in 2021 for computer science class. To think this video would help me for this long.

[@bundokman]

Lol...I'm in the same boat, went back to school for Comp Sci, I forgot how bad professors can be in teaching anything. Thank God for this guy.

[@DisguyRanger]

Thank you so much for helping me understand induction so quickly. You're awesome!

[@MattUK]

Yaaaaaay, I've spent months listening to my teacher telling me the same thing, and I didn't understand any of the transition between assumption and proving, but this did it :) now lets hope I can master it for the exam in 3 weeks...

[@jessicakameniteulawo7226]

PATRICK YOUR THE BEST EVEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEER!!! THRO UR EXPLANATIONS I UNDERSTOOD IN SOME MINUTES WHAT TOOK ME 5 HOURS TO CRAM.

[@pimpintad]

You are awesome. I really had a difficult time understanding induction and you were able to clear so many things up. Thanks a lot!

[@nonceprogrammer]

oh my god, i'm getting addict to your videos! i cant stop swatch!! The letters, the paper, the marker!! it's addictive!

[@trevorlinet]

Thank you so much! You helped me 4.0 Calc I, 3.5 Calc II, but now I'm struggling with Discrete Mathematics. You just explained a concept that made 0 sense to me when my professor explained it, in 3 short videos. Thank you so much.

[@TheHeartOvALion]

ive no way of explaining how amazing you explained that..if only math teacher were more like you....great job!

[@nigelsterne1788]

Ive been searching for hours and this is the only vid that made sense, thanks!

[@MaciBleue]

I just found this channel!!! Thanks so much man; I might just pull a B instead of an F on my exam tomorrow thanks to you 🙏🏾🙏🏾🙏🏾

[@rosemarypatronellamatura4689]

well done that was excellently done

[@daraoyedijo]

And the "seasoned" prof that taught me couldn't explain this properly for two 3hr classes and even after going to his office hours. Smh. Great Job Patrick!

[@LeandroQuibemMagnabosco]

Thank you for this video. You are really good at explaining clearly what you are teaching.

[@blkchrm77]

4 lectures on this stuff and I didn't get it. After watching your video, I didn't know it was actually that simple. Thanks

[@jifroudi]

thank you so much bro, just this one video cleared everything up for me, our prof, is just not that clear in class and rushes through everything. :)

[@kurchak]

Mathematical Induction is so beautiful.

[@OgllyBoogly]

Exam in 2 hours on this? No problem mlg teacher here.

[@OgllyBoogly]

pulled out with an 83% pretty good seeming how the class average was a 64% :D

[@nogeniuos]

nice, hopefully my exam only has one of these questions bc everything prior is really easy.

[@jazzm5557]

LMAO I've got an exam in 2 hours on this! Patrick videos still goin strong

[@joeyGalileoHotto]

Bro if I had Patrick as a professor, I'd get straight A's and change my major to math

[@kevincherry6037]

How did your exam go

[@exploreethiopia3376]

These video is good for me . Thank-you

[@Mr_KingsMentality]

THANK YOU! I am being tested on this tomorrow, and now I understand the concept.

[@mariapersaud9685]

omg you sweet angel thank you for existing, because of you i have a chance at passing my quiz tomorrow

[@ericmeyerhuber6748]

Nice clear example and explanation. I knew it wasn't hard, but the book and prof did not do what you did. Thank you very much.

[@randyt700]

thanks for taking the time to do this! can you upload a video on strong induction as well?

[@noblessus]

Very nice explanation. Any chance you'll do some examples showing Strong Induction a.k.a. the second principle of mathematical induction? I'm really struggling with that one. Thanks for your great videos!

[@warren010h]

Thanks for great vid!! Have a midterm exam in my data structures class this upcoming monday, and just a few days to get this down packed. thanks again!

[@AstralAbraxas]

best explanation of mathematical induction i have ever seen.

[@nonceprogrammer]

oh my god, i'm getting addict to your videos! i cant stop swatch!!

[@majesticbarrack5506]

wow amazing i can't understand it in a whole hour in my class which you teach me in just 6:29 minuts. and my answer is also(5k^2+13k+8)/2 in both side

[@newgame99]

Thank you very much!! It was a great help for my discrete math class!!

[@casparclaessen2288]

Thanks a lot because of you I have courage and hope that I will pass my exam tomorrow

[@snake1625b]

I wish he wasnt left handed, his hand often gets in the way. good vid none the less

[@windowslogo3577]

+John Fernandez Actually if he was right handed there would be a great chance that he wouldn't be making this video.

[@DEEPAKKUMAR-vv9vg]

exactly

[@veryallen3]

albert einstein was left-handed for your information

[@williamtylerwillis6417]

Right ... fucking left handed weirdos

[@charlesjsescoto]

If he was Not, he can't teach us, because it's the source of knowledge (LH)

[@rleo015]

This video was very helpful, you've done a great job explaining. Thank you!

[@itsmrcontrol1]

6:30 he was writing just an example no wonder why everybody hates math but thank you for your video I've learned this gigantic example by 630 times watching it

[@kattz9051]

I'm so happy that your hand-writing is actually legible!!!

[@warrenbinder3612]

8 years later, thank you!

[@Sara-nf7mq]

YOU JUST SAVED MY LIFE WITH THIS VIDEO!!!!

[@dillonredd9682]

you're a wizard Patrick! thank you so much for your videos.

[@patrickjmt]

@carlitozway57 ha, i dont publish the screw ups, but believe me, they are there! i have thought about having a 'blooper' reel. it would be profanity laced as well : )

[@sebastianvargas2159]

This video was quick yet extremely helpful. Thanks!

[@RenderedGames]

It's because we assume true for n=k (the line with 4+9+14+19+...+(5k-1)) = k/2(3+5k). Therefore, if you substitute in for the 4+9+14+19+...+(5k-1) bit for n=k+1, then you get the k/2(3+5k).

[@Austenh22]

very well done video, I was struggling with induction and your video really helped. Thanks a bunch!