Mathematical Induction Practice Problems

  • Published on Feb 20, 2018
  • This precalculus video tutorial provides a basic introduction into mathematical induction. It contains plenty of examples and practice problems on mathematical induction proofs. It explains how to prove certain mathematical statements by substituting n with k and the next term k + 1. Examples include arithmetic sequences and exponents.

Comments • 140

  • Paola Castro
    Paola Castro Day ago

    I have a test today I’m this is an hour

  • Gilma Ferrer
    Gilma Ferrer 2 days ago

    JG, you are the best, thank you for doing this!

  • RADO
    RADO 5 days ago +1

    Math means mental abuse to humans

  • Jonathan Villa
    Jonathan Villa 6 days ago +17

    Who else is here because their discrete math professor can not explain this stuff well?

    • Ellie Mandy
      Ellie Mandy 2 days ago

      Jonathan Villa sweet, i go to Georgia Gwinnett College.

    • Jonathan Villa
      Jonathan Villa 2 days ago +1

      Ellie Mandy I go to Lewis University In Illinois!

    • Ellie Mandy
      Ellie Mandy 2 days ago +1

      hahaha me! what college do you go to?

  • Mark G05!
    Mark G05! 8 days ago

    3:45 I still don't understand why did you choose four

  • Victor Harris
    Victor Harris 10 days ago +2

    I came here because I fell asleep while my teacher discusses this one

  • Torment
    Torment 10 days ago

    great examples. where are more of proof type problems in your channel?

  • Jp Tayco
    Jp Tayco 11 days ago

    you're better to teach than our teacher which is we paying her for lessons

  • Peyton Butler
    Peyton Butler 12 days ago

    literally want to cry you saved my ass thank you

  • A7md_XgamZ
    A7md_XgamZ 13 days ago +1

    I didn’t understand any of this . I spend a year to understand induction but I couldn’t 😩😩😩😩😩😩 FUCK IT

  • Ahmed Ismail
    Ahmed Ismail 16 days ago

    i just found heaven here

  • Aimee Finlayson
    Aimee Finlayson 23 days ago

    12.39 what happens to the (k+1)^3 it just disappears

    • DeviousShadows
      DeviousShadows 19 days ago

      He factorized out the (k+1)^2. 4(k+1)^3 / (k+1)^2 = 4(k+1)

  • Aprishiela Hartono
    Aprishiela Hartono 27 days ago

    what a crystal clear explanation. Thank you very much :)

  • illlanoize23
    illlanoize23 29 days ago +1

    I get this shit here but I know when it’s time for the test I’m going to forget literally everything. Ugh I’m so bad at factoring. Don’t take years between math classes people otherwise you forget stuff

  • Veronika Lysenko
    Veronika Lysenko 29 days ago

    As this was review for me I sped up the video ×2. Otherwise you are waiting for him to erace the notes or watching simple mathematics. Overall I found this video very insightful.

  • Gemma Baloloy
    Gemma Baloloy Month ago

    at 8:25 why is 4 over 4 got cancelled...i thought 4(3)^2 = 36 before dividing it to 4??? help pls

    • migs sants
      migs sants 29 days ago

      It would actually get you the same answer... which is 9. the reason you divide by 4 is because you are multiplying the 3^2 already. So it would just cancel out

  • Hey! I't Faye
    Hey! I't Faye Month ago +1

    Our precalculus teacher taught that we needed to add the lcd to both sides

  • Ace Go
    Ace Go Month ago

    You are always a savior.

  • Elijah Blake
    Elijah Blake Month ago +1

    Here you are saving the day again. Just like the last two years of my math classes.

  • Rodney Muganzi
    Rodney Muganzi Month ago

    I love this dude

  • Bahar Osman
    Bahar Osman Month ago

    Math induction is meaningless i hate it so much!!!!!!

  • Stephanie Soto
    Stephanie Soto Month ago +1

    Wow this helped so much! Thanks again for all the videos I have watched from your channel that have helped me throughout the semester! You saved me! Haha

  • Tresh Dorol
    Tresh Dorol Month ago

    Super effective neto💖

  • Ab Abdi
    Ab Abdi 2 months ago +1

    dont get how u expanded on 13:12

  • megha tirkey
    megha tirkey 2 months ago +1

    Can you please make a video on complex functions

  • major2 colonel
    major2 colonel 2 months ago

    WOW i understood in no time great job mr tutor

  • Zachary Tabz
    Zachary Tabz 2 months ago +10

    "what still searching for math help? are videos from 2007 really help you?"jajaja lol

  • Gabriel idowu
    Gabriel idowu 2 months ago

    thanks so much for helping me out

  • Eniola Adejumo
    Eniola Adejumo 2 months ago +3

    Thank you , your video was beyond helpful, I’ve been trying to learn this for quite a while now and in just under 18 minutes it’s all clear. Thanks again

  • A. Abduba
    A. Abduba 3 months ago

    Very helpful video......Thanks man

  • MALUMI Blessing Aderinke
    MALUMI Blessing Aderinke 3 months ago +1

    This made my day after struggling with this on my own...

  • luis soto
    luis soto 3 months ago

    thanks to your videos I passed my math classes

  • stellus francis
    stellus francis 3 months ago

    So.. Can we add 4 to both the sides?? Or can we add whatever no that is given...?? There isn't any problem ryt? !!

  • Tin A
    Tin A 4 months ago

    Thanks man you're a lifesaver

  • Lexer Guevara
    Lexer Guevara 4 months ago

    what app are you using sir thankss

  • Lexer Guevara
    Lexer Guevara 4 months ago

    thankss sir

  • anuradha ramji
    anuradha ramji 4 months ago +6

    Simple and easy explanation.Thanks to people like you ,maths is still interesting..praise God

  • Obada Zerkly
    Obada Zerkly 4 months ago


  • The Geek Site
    The Geek Site 5 months ago

    What is the use of this thing ?

  • Threelly AI
    Threelly AI 5 months ago

    So hyped...

  • Daniel Adewunmi
    Daniel Adewunmi 5 months ago

    Thanks you help me a lot

  • Rk Shuvo Raj
    Rk Shuvo Raj 6 months ago

    Thank u sir

  • mishlol123
    mishlol123 6 months ago +1

    okay you deserve a sub bro
    this helped me alot
    thank you very much

  • Moaz El-sawaf
    Moaz El-sawaf 6 months ago

    Thanks sir

  • Eyad tube
    Eyad tube 6 months ago

    hello the organic chemistry am eyad tube my chanel contient are the same as you on mathematics please joine my home and share my video am already joine your chanal

  • Allan Onyango
    Allan Onyango 7 months ago +1

    fantastic explanation thank you so much

  • Feel Physics
    Feel Physics 7 months ago +2

    !!!!Induction doesn't really serve as a proof.
    It can be used as a first check for the formula.
    1)A formula that is invalid by induction has no chance of being true.
    2) But even if some formula passes this test doesn't necessarily mean it is true.
    Let say u write the formula for summation
    (1)^3+(2)^3 ....(n)^3 = n^2(n+1)^2/4 + c (c is any random constant)
    Induction says that it is right for any value of c but it is not true.

    • Karen Boxenhorn
      Karen Boxenhorn 2 months ago

      there is a difference between induction and mathematical induction

  • SunCityRick
    SunCityRick 7 months ago

    After a number of youtube vids and books this video finally helped me intuitively understand induction, thanks!

  • kalpana varsha
    kalpana varsha 7 months ago

    Can you say clearly the reasons

    • Karen Boxenhorn
      Karen Boxenhorn 2 months ago

      mathematical induction has two steps:
      the basis, where you prove that the rule is true for a 'first' element (n=1).
      and the induction, where you prove that, assuming the rule is true for an element (n=k), it is true for the next succeeding element (n=k+1).

  • NetworkRob
    NetworkRob 8 months ago

    Amazing explanation step by step.

  • Vikas Kumar
    Vikas Kumar 8 months ago +1

    Thank u sir your explanation helped me a lot thank u so much😙😙😁

  • Cedrick Cruz
    Cedrick Cruz 8 months ago

    in your 3rd example on 2(2^k)-1 part.. The answer should be 4^k+1-1 isnt it? because what you did in your sub example is a variable but in the actual example you gave you used a number. Could you please further explain to me how that happened? Thank youu!

  • Kyla Byun
    Kyla Byun 8 months ago +1


  • NØ ØNE
    NØ ØNE 8 months ago +1

    You're the BEST

  • Joy Lee Moorndoz
    Joy Lee Moorndoz 8 months ago

    This is great!.

  • Brittany Chan
    Brittany Chan 8 months ago

    okay but like why is this theory/ how they replace the k value with the previous answer so smart?

  • Maimai Halid
    Maimai Halid 8 months ago


  • BHD TV
    BHD TV 9 months ago

    And in 12:00 how did you subtract 2 from (k+1)³ to give (k+1)
    Where did the ² come from?

    • Robert Baker
      Robert Baker 9 months ago +1

      He factorized by dividing by (k+1)^2, think of it as a^3/a^2, when the base of two numbers are the same and you divide them you subtract the indices. Since both bases are (k+1) he subtracted the indices of (k+1)^3 and (k+1)^2 leaving (k+1)

  • BHD TV
    BHD TV 9 months ago

    The 3rd equation was😏 that's not even how the law of indices works🙄... But thanks bro I never understood mathematical induction until today

  • Zaheer Ahmed
    Zaheer Ahmed 9 months ago +10

    Thanks man I pass my discrete Math class because of you . you make things very clear and easy to understand