Proof by Induction - Example 1

  • Published on Aug 3, 2010
  • Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) !! Proof by Induction - Example 1

Comments • 576

  • syed saba
    syed saba 4 days ago

    Amazing.. Video 👌👌👌👌

  • Inayat khan
    Inayat khan 6 days ago


  • Garen Kantarci
    Garen Kantarci 7 days ago

    Has anyone told you that you are a god among men?

  • mqhele mguni
    mqhele mguni 22 days ago

    2019 at PJMT BUSE University says Patrick is the TRUTH!

  • Simi S
    Simi S 28 days ago +1

    Anyone noticed that he is left hand ed

  • Greggie Pattry
    Greggie Pattry 2 months ago

    do i always assume the statement is true?

    • Lars K
      Lars K Month ago

      You assume the statement is true. For any natural number k the statement works. So IF the thing you assumed is true, then the statement also works for k+1. Therefore, since you have already proven that k=1 works, your assumption is correct. And therefore you can conclude the statement works for 2, 3, 4...
      Assuming that the statement is true is vital in this case.

  • Thifal Raniah
    Thifal Raniah 2 months ago

    Thank you so much! 🔥💛

  • Sunil nair
    Sunil nair 2 months ago +1

    Tnx sir😊😊

  • Josh Lipovetsky
    Josh Lipovetsky 2 months ago

    Thank you!

  • stellus francis
    stellus francis 3 months ago

    Thnx a lot.......

  • Helen Jay
    Helen Jay 3 months ago

    Thank you very much for this video I'm doing my maths exam revision now.

  • arletd paucar
    arletd paucar 4 months ago

    wow I didn't get it until I saw your video! very helpful

  • Frank V
    Frank V 4 months ago

    Halfway through the video and all I keep thinking is, "So this is what people have to deal with watching me write something left-handed? My hand covering up what I'm writing until I'm done?"

  • Sebastian Suarez
    Sebastian Suarez 4 months ago

    Why do you add 5(k+1)-1 to the left side and not just 5(k+1)??

    • Helen Jay
      Helen Jay 3 months ago +1

      The K plus 1 was shoved into the equation.

  • Elvin Gamers
    Elvin Gamers 4 months ago +1

    Hello 2010

  • Stephen Mack
    Stephen Mack 4 months ago +2

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

  • Landon Shenberger
    Landon Shenberger 6 months ago


  • Divya Shukla
    Divya Shukla 6 months ago


  • PicledH
    PicledH 6 months ago

    what is the additional term for??

  • Queso Dilla
    Queso Dilla 6 months ago

    Too bad this would get me marked in my class as my teacher counts 0 as a natural number which disproves the base case lol

  • crissy newton hwaaa
    crissy newton hwaaa 6 months ago

    this is simply the best keep on keeping on

  • Fade
    Fade 6 months ago

    Goddamn, I should've watched this video instead of rereading the same section from the textbook for hours.

  • Sam Saghafi
    Sam Saghafi 7 months ago

    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 TheXvid tutor. Thank you

  • Nigel Sterne
    Nigel Sterne 7 months ago

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

  • Chuyu Liu
    Chuyu Liu 7 months ago

    Thank you

  • Joseph G. Hotto
    Joseph G. Hotto 9 months ago

    *breathes a sigh of relief*

  • Victor Tsenov
    Victor Tsenov 10 months ago

    thank you kind sir.

  • ToXiiC NebuLa
    ToXiiC NebuLa 10 months ago

    Lol, this may seem weird but I find it satisfying to watch and learn from Left-handed mathematicians. Their hand usually is in the way of some of the problem whilst writing it out, therefore, it gives me the logical reason of being last to answer for being the only one to go back and read the problem once more. ☺

  • Xylok
    Xylok 10 months ago

    i bet i can become three times better at math than you before you can eat and transform into nothingness a full size universe!

  • Xylok
    Xylok 10 months ago

    18 seconds in; got some glimpse of some of the hint of the gist of the depth; laughed hard, kept watching on, finished the vid, wrote this comment, went on with my mediocre hair day to ongoing presents.

    ORACLE OFFICIAL 10 months ago

    i'll teach you to be right handed cz your left hand really really really sucks..!

  • aeroO bics
    aeroO bics 11 months ago +1

    Induction must be the least elegant type of proof. We are assuming to much. And of course the result will end up correct. P(m) + X will always add up to P(m+1)

  • n n
    n n 11 months ago

    Wow couldn't be any easier

  • Eric Meyerhuber
    Eric Meyerhuber Year ago

    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.

  • Meg Anedez
    Meg Anedez Year ago

    Pls answer me why there’s additional i dont get it

  • Antonio J G-B
    Antonio J G-B Year ago

    Patrick I'm sure you get a lot comments praising you so instead just get yourself an ice cream for your well put explanation on the concept of proof by induction.

  • Antonio J G-B
    Antonio J G-B Year ago

    I'm confused as to why he went from 4+9+14+19+...+(5k-1) into (k/2)(3+5k)

    • Antonio J G-B
      Antonio J G-B Year ago

      I figured it out, he replaced it because we substituted with the P(k) expression from our assumption.

    THE ROYALS Year ago +2

    sir where is 13k coming from and why

  • Nemisha Chris
    Nemisha Chris Year ago

    Why we adding additional term in left hand side

  • Karabo Monaiwa
    Karabo Monaiwa Year ago

    Yet you save my life again...

  • Honey Claire Gemeniano

    I dont get it. Sorry for my stupidity

  • Twisting Tiger
    Twisting Tiger Year ago

    I wish he wasn't left-handed. His left hand acted as a barrier 😕

    • patrickJMT
      patrickJMT  Year ago

      yea, it does get in the way sometimes. i try to be conscious of it but often forget

  • Dexter Nicer
    Dexter Nicer Year ago

    where did you get the times 2 in 4k/1?

  • Ahmed Mirza
    Ahmed Mirza Year ago

    Where is 5k gone plzz tell me

  • Yousif Sirrieh
    Yousif Sirrieh Year ago

    mnwer ya gale

  • Darknavy42
    Darknavy42 Year ago

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

  • Aimee W.
    Aimee W. Year ago

    just want to let you know that I'm in love with you.

  • Blo op
    Blo op Year ago


  • Warren Binder
    Warren Binder Year ago

    8 years later, thank you!

  • Robert Wagner
    Robert Wagner Year ago

    Good stuff

  • Chandru .A
    Chandru .A Year ago

    We should write in your right hand

  • sophie ng seah
    sophie ng seah Year ago

    useful video! Thumbs up!

  • Nicholas Henderson

    My discrete math assignment thanks you

  • Pedro Torchio
    Pedro Torchio Year ago

    Naturals bigger than zero, right? Or are you considering Natural numbers as positive Integers? Thanks for the vid

  • siyethemba simlindile

    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

  • Jack Daniel
    Jack Daniel Year ago

    Damn, your writing is so clear and fast!

  • Proper way to live by giving

    James 2: 6-7 But you have dishonored the poor. Is it not the rich who are exploiting you? Are they not the ones who are dragging you into court? Are they not the ones who are blaspheming the noble name of him to whom you belong?

  • Caspar Claessen
    Caspar Claessen Year ago

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

  • Kameryn Cherry
    Kameryn Cherry Year ago +13

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

  • Huckleberry Lover