Mathematical Induction Examples

Learn how to use Mathematical Induction in this free math video tutorial by Mario's Math Tutoring. We go through two examples in this video.
0:30 Explanation of the 4 Steps of Mathematical Induction
2:12 Example 1 Mathematical Induction Problem
2:35 Step 1 Show True for n=1
3:22 Step 2 Mathematical Induction Assumption
4:19 Step 3 Show True For n=k+1
7:44 Step 4 By the Process of Mathematical Induction...
8:35 Example 2
13:20 Difference between the meaning of k and n
Looking to raise your math score on the ACT and new SAT?
Check out my Huge ACT Math Video Course and my Huge SAT Math Video Course for sale at
mariosmathtutoring.teachable.com
For online 1-to-1 tutoring or more information about me see my website at:
www.mariosmathtutoring.com
* Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below)
www.mariosmathtutoring.com/fre...

[@whitelined2]

University level student here. Very clearly explained video, thank you. Some textbooks explanations are like a magic trick - like it magically works out without seeing what happens in between.

[@MariosMathTutoring]

+whitelined2 glad my video helped clear up any confusion or left out steps as you mentioned.

[@ZackV2496]

hhahaha true

[@yudaikoyama3276]

Thank you professor X

[@thedownzguy]

This the best comment on KZbin.

[@hopeenvy]

I laughed so hard I forgot how unbearable university is

[@aquinoaeroon-s2058]

HSHAHAHAHHA

[@abdulomar2351]

It was very helpful, almost gave up until I watched this one. Thanks so much, sir.

[@MariosMathTutoring]

You’re welcome Abdul!

[@eavyjunior9485]

I love this man's videos, his humble expression and detailed explanations are extra ordinary

[@francescovanspronsen2377]

Best one out there especially by mentioning the 4 steps! Thanks so much man.

[@esouvedot6790]

Thank you so much for this!! I'm still in high school, for our Pre-Calculus and it's basically self-learning but this just made me understand it more. Thank you very much!!💞

[@waltz9230]

You're the only person that explained this in a way I could understand. Thank you!

[@MariosMathTutoring]

Glad it was helpful!

[@tanuki_zero]

Was unable to perform induction for my college Discrete Math course, now I can do it with ease. Thank you :)

[@MariosMathTutoring]

You’re welcome!

[@ivanzambrano6166]

Hi Mario, You are an excellent tutor or teacher, very detailed, very thorough …..as it is supposed to be. Congrats! 6/11/2022

[@noorrafique8355]

Am from Pakistan.........In my course math 201 23rd lecture i can't understand that topic of induction but now i,m completely understand the mathematical induction thank u sooo much sir your explanation way is awesome.....ALLAH BLESS you with success Aameeen

[@kimyates6561]

Out of all the induction videos I've watched this ones the best tyty

[@MariosMathTutoring]

Your welcome! Glad my video helped you!

[@ponimurye5520]

thank you so much! you really simplified it and now I understand. i can finally do my homework!

[@DJAtomic5]

Thank you very much for the easy video! My math professor always showed too many steps and was constantly getting lost, your easy 4 step explanation really helped me understand this topic!

[@MariosMathTutoring]

Awesome! Glad my video helped simplify this concept for you!

[@martinsmarcis963]

Couldn't understand for couple hours and then learned in 12 minutes, thats nice. Thank you soo much!

[@MariosMathTutoring]

You’re welcome! Glad my mathematical induction video helped you!

[@Alfredo5883]

The Best explanation on Mathematical Induction! Thank you Sir!

[@polarpanda2001]

Love you man, helping me pass my pre calc test that I have next period, thnx 👌

[@katerinapress9982]

omg my tutor has been trying to teach me this but I couldn't understand until now, thank you so much!

[@katerinas5736]

Great explanation! Thank you!

[@chrisogonas]

Great and clear illustration! Thx

[@SheidaR]

This is the only video that helped me. Thank you so much!

[@jessicaasomugha554]

I'm so glad I found your Chanel math is so much easier with the right explanation

[@gaashahuundamissaw3340]

Teacher of the world. I love your courses much

[@robertkamanga]

Now l understand this concept, thank you very much !

[@getahuntegafaw6150]

Appreciate your lecturinig keep it up...amazing You are so dynamic

[@licahdaizy734]

THANK YOU SO MUCH SIR !!!!!!! after watching so manyyyyyyyyy videos your explanation is the BEST!!!!!!!!! thank you a lot sir ,' have a nice day!!

[@MariosMathTutoring]

Glad my video helped you Licah!

[@licahdaizy734]

you are welcome sir , maybe if you can make more videos regarding this topic but in Sigma and inequalities.... harder examples ... thank you!!

[@sallaklamhayyen9876]

great explanation thank you so much so i'm subscribed

[@stephenbwalya1168]

Indeed this is the best one, good teacher. i have enjoyed the lesson so much.

[@MariosMathTutoring]

Glad you liked the video Stephen!

[@zaharanakacwa9587]

Thanks for that pure knowledge explanation

[@ackerman258]

BIG LEVEL HELP PROFESSOR MARIO, GREETINGS AND THANKS FROM TUSCON ARIZONA

[@networkmarketingandfun2712]

very best way to explain... thank u Mario

[@MariosMathTutoring]

Your welcome. Glad you liked the video.

[@TurboNrrdFPV]

This really, really helped...THANK YOU SIR!!!

[@MariosMathTutoring]

Your welcome!

[@hamade7997]

Clearest tutorial I have found on this subject, thank you very much sir!

[@MariosMathTutoring]

+Hamade Moodie your welcome!

[@BrightAcademy12]

Yeah! It really helped me. Thanks

[@kvng_Edwin]

This is an awesome tutorial.. i understood this now thanks alot

[@MariosMathTutoring]

Great! Glad my video was able to help you!

[@leandroevangelista4660]

thanks for this video, it's exactly what i was searching

[@MariosMathTutoring]

You’re welcome Leandro!

[@dulcevazquez4020]

thank you so much.. you made it look so easy!!!!

[@MariosMathTutoring]

You’re welcome Rodriguez! Glad my video helped you!

[@ProKashif]

i was confused about this topic but now its looks so easy . thank you sir

[@MariosMathTutoring]

You’re welcome Kashif! Glad my video helped clear things up!

[@StarRose137]

you explained it better than my professor! Thank you!

[@kingmannau1376]

Best explanation. I wasn't taught like that.

[@samsaghafi4876]

Thank you so much you are an amazing tutor

[@MariosMathTutoring]

Glad you liked the video I did on mathematical induction Sam!

[@geraldillo]

You made it easy to understand, thanks!

[@MariosMathTutoring]

Glad my video helped you!

[@bonganimafemani3156]

thank you so much!!!!!!

[@harriethaisty4101]

Awesome, thank you!

[@MariosMathTutoring]

Your welcome!

[@sleepyman5321]

At 6:22 I don't understand how to get from 3K(K+1) + 6(K+1) to 3(K+1)(K+2)? I can get from 3K(K+1) + 6(K+1) into 3K^2 + 9K + 6K and also I can see that 3(K+1)(K+2) is also 3K^2 + 9K + 6K, but what I do not understand is how can I get straight from 3K(K+1) + 6(K+1) to 3(K+1)(K+2)? I know it is some simple math trick, that everyone (except me) knows by heart but it would have taken like 30sec to explain it in the video.

[@mr.perfect8750]

10 times much better explanation than my college maths teacher. Thanks a lot and now I subscribed you🙏

[@MariosMathTutoring]

Glad you liked the explanation! Welcome to the channel!

[@Animalkingdom.x]

great ❤❤

[@networkmarketingandfun2712]

steps are very useful..

[@juberpansare9272]

I had a maths test and it went pretty smooth... If only I could thank you for your wonderful teaching method.... Lots of love from India.... You are doing a great job sir ;)

[@MariosMathTutoring]

Thanks! Glad my videos are helping you! Glad your test went well!

[@mogli3leo]

Mario saves the day once again!

[@MariosMathTutoring]

Glad you liked the video!

[@aratitotad9775]

Thank u sir u explained why to take k and k+ 1

[@durumargaret9915]

Thanks sir God bless you

[@Nuel_Take_Profit]

Incredible

[@xxnikixx9440]

you have saved my life Mr Mario sir

[@Buzzehxcx]

Thank you! Very Clear examples!

[@MariosMathTutoring]

Your welcome! Glad my video was clear!

[@husseincheaito28]

I love you Mario.

[@taneeswaseem7119]

Very clear explanation thank you 😤me being a math minor I still hate how textbooks do it

[@adamahmed973]

Thank your, Sir!

[@MariosMathTutoring]

You’re welcome Adam!

[@aliyaali9421]

very nycc....helped me...thnk u sir

[@MariosMathTutoring]

Your welcome

[@zitlerthebandit9596]

Very helpful ,thax man

[@MariosMathTutoring]

You’re welcome!

[@Alicia0Cramel]

Incredible.

[@MariosMathTutoring]

Glad you liked the video Sabrii!

[@neymarjunior7273]

Sir u are awesome I understand math induction

[@MariosMathTutoring]

Glad my video helped you!

[@monettedyar2837]

Thanks!

[@MariosMathTutoring]

Thank you!!

[@tabibhassan3376]

Thanks sir. It was helpful.

[@MariosMathTutoring]

You’re welcome Tabib!

[@mohammadaxelariapaskha9791]

Thanks

[@harrywatson4256]

You are amazing but your maths question is more amazing

[@ashishacharya9015]

Thank you 🙏

[@MariosMathTutoring]

You’re welcome Ashish!

[@sudha5353]

Good work I can understand

[@MariosMathTutoring]

Awesome! Glad that helped you Sudha!

[@devpetdev]

I have a question...although I know it is unnecessary in this particular problem, but is it logically/mathematically valid to apply an operation on both sides of the equation in step 3 in order to simplify? For example, could I multiply the LHS and RHS by 2 if I wanted to "eliminate" the 2 from the RHS divisor. I know in this particular problem it doesn't help and we wouldn't do that, but my question is for other problems where that might make sense, is it at least a valid operation?

[@quranication]

Thank you...

[@MariosMathTutoring]

You’re welcome Nms Sakib!

[@kirtimishra9615]

Thank you sir

[@MariosMathTutoring]

You’re welcome Kirti!

[@seraph.winter7894]

Is it ok if we put step 2 and step 3 as one step together?

[@jamesrobertson9149]

very helpful. thanks.

[@MariosMathTutoring]

Your welcome!

[@Green.n.Purple]

this man is a god at teaching

[@MariosMathTutoring]

Glad you like my teaching style!

[@saleemismailkugu2426]

Please sir help me solve this question. I'm having difficulties here trying to solve it. x-12, 3x-2/7, 3x+2/7, Bx+6. What is the value of B.

[@neilkozlowski8023]

beautiful

[@thenvsnowtv1811]

thanks a lot man

[@MariosMathTutoring]

Your welcome!

[@CorpseGr1nd90]

Thank you Mario, this really helped me out!

[@MariosMathTutoring]

+franku-san great! Glad my video helped you!

[@reazulislamrifat8479]

i can't explain you sir how much i wanna give thank you.

[@MariosMathTutoring]

So nice of you

[@analimbeytv6312]

Nice

[@maxima4116]

is the n=k+1 in the 3rd step constant? like every problem its always show true for n=k+1?

[@jadenpieterse7056]

yes purple moon , for every problem you assume that or you take true for n=k+1

[@ericlopez3067]

In the first example at 7:14 why is it (K+2) and not (K+1)? I don't understand the factoring process and how it came to be 2 during that process. Or are we just to assume it factors out to 2?

[@coolarman]

So what he did was he factored (k+1) right. After he did that, he had a 3K+6 left over so the faction would look like (k+1)(3k+6)/2. From there he then factored a 3 from from (3k+6) which gave him (k+2)

[@dougrose4393]

Thanksssss

[@MariosMathTutoring]

You’re welcome Doug!

[@msaeedmsaeed1881]

Very nice

[@MariosMathTutoring]

Glad you liked the video!

[@BsmTwo]

Thank you so much. I wish I was giving you 20k a semester instead of my professors

[@MariosMathTutoring]

Happy to help!

[@user-fe9mr8sp1j]

impressed

[@arsimxhi7984]

thanks professor X form pakistan

[@Dana-wl2sk]

WOOOOOW

[@melissah6388]

THNX GANG

[@kashifmurtaza5010]

First condition is true for n=1 If we take 2,3,4 then it's not true?? Plz reply

[@MariosMathTutoring]

Kashif, are you referring to an example in the video or an example you are working on?...keep in mind that the formula on the right side of the equation in my video represents the SUM of however many terms...the formula on the left is an explicit formula to find a specific term. If you add up the first 3 terms on the left(for example) and substitute 3 into the right side of the equation for n they should equal each other. Hope that helps you!

[@kashifmurtaza5010]

Mario's Math Tutoring Sir I am just asking to u that if we take n=2 or any positive integer rather than 1.. Is that true or false? Sir plz reply

[@dedoomx6172]

My n=1 doesn't work. I mean, it goes like 5 = -5. And so on, all of em arent equal. Does that mean I don't need to proceed on step 2 because there's no sense anymore? Doesn't equal at first at all.

[@Altair.1187]

Thank you king Mario, unfortunately in exams we get more complicated problems ...

[@mohammadaghshal9048]

hi, there is a question that bothers me and i cant find any solution for it anywhere, its from a analys math book, can you pleas help me with it? :if f(n) means: "(3^2n)-8n+1 is divisable by 64", and if f(n) is true, then prove that f(n+1) is also true. then prove that in fact the proposition "for every positive integer n, (3^2n)-8n+1 is divisabel by 64" is false!. the prove should be only with induction and no series or sequences. just induction, and the falsity of the proposition in the problem does not mean the problem is false, but it is false on a purpose(for induction purposes i think!). thanks in advance for any help.

[@ashercrix1858]

How to make a problem with your own sir??

[@cyclofish1185]

can anybody explain the second example? why is the left side 2^0 instead of 1 + 2^0?

[@umendrashukla2978]

..Coz in the given series the n^th term is (n-1). So we write 2^(1-1) i.e. 2^0 =1. Hope now u got this.

[@saifalshamsi8627]

Legend

[@MariosMathTutoring]

Glad you like my videos Saif!

[@ayubsamuel100]

Mario, help me out with this one,1²+2²+3²+4²+...+(2n)²=[n(2n+1)(4n+1)]/3

[@bleon_co]

Wondering why the + changed to multiplication

[@JSbean]

can someone please explain how he got 3(k+1)[k+2]/2 7:15

[@TheShuper78]

n=k+1 so when you plug it in n+1 ----> (k+1)+1= k+2

[@abdullahasif7992]

Jordan S You can do it this way: 3k(k+1) + 6(k+1) /2 (3k+6)(k+1) /2 3(k+2)(k+1) /2 Rearranging: 3(k+1)(k+2) /2

[@Bakhtiar.Khetran]

Was it that easy ?? and i just feel shame on myself i could never understand this...... Thank you sooo much ....

[@Bakhtiar.Khetran]

because it was never explained like this....❤❤😍😍😍😘😘😘

[@MariosMathTutoring]

Glad you liked the video!

[@oneaboveall6239]

is there is any use of M.I in real life