# Mathematical Induction Practice Problems

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• 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.

• Paola Castro Day ago

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

• Gilma Ferrer 2 days ago

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

• RADO 5 days ago +1

Math means mental abuse to humans

• Jonathan Villa 6 days ago +17

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

• Ellie Mandy 2 days ago

Jonathan Villa sweet, i go to Georgia Gwinnett College.

• Jonathan Villa 2 days ago +1

Ellie Mandy I go to Lewis University In Illinois!

• Ellie Mandy 2 days ago +1

hahaha me! what college do you go to?

• Mark G05! 8 days ago

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

• Victor Harris 10 days ago +2

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

• Torment 10 days ago

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

• Jp Tayco 11 days ago

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

• Peyton Butler 12 days ago

literally want to cry you saved my ass thank you

• 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 16 days ago

i just found heaven here

• Aimee Finlayson 23 days ago

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

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

• Aprishiela Hartono 27 days ago

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

• 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 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 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 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 Month ago +1

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

• Ace Go Month ago

You are always a savior.

• Elijah Blake Month ago +1

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

• Rodney Muganzi Month ago

I love this dude

• Bahar Osman Month ago

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

• 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 Month ago

Super effective neto💖

• Ab Abdi 2 months ago +1

dont get how u expanded on 13:12

• megha tirkey 2 months ago +1

Can you please make a video on complex functions

• major2 colonel 2 months ago

WOW i understood in no time great job mr tutor

• Zachary Tabz 2 months ago +10

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

• Gabriel idowu 2 months ago

thanks so much for helping me out

• 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 3 months ago

• MALUMI Blessing Aderinke 3 months ago +1

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

• luis soto 3 months ago

thanks to your videos I passed my math classes

• 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 4 months ago

Thanks man you're a lifesaver

• Lexer Guevara 4 months ago

what app are you using sir thankss

• Lexer Guevara 4 months ago

thankss sir

• anuradha ramji 4 months ago +6

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

• Obada Zerkly 4 months ago

thanks

• The Geek Site 5 months ago

What is the use of this thing ?

• Threelly AI 5 months ago

So hyped...

• Daniel Adewunmi 5 months ago

Thanks you help me a lot

• Rk Shuvo Raj 6 months ago

Thank u sir

• mishlol123 6 months ago +1

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

• Moaz El-sawaf 6 months ago

Thanks sir

• 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 7 months ago +1

fantastic explanation thank you so much

• 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 2 months ago

there is a difference between induction and mathematical induction

• SunCityRick 7 months ago

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

• kalpana varsha 7 months ago

Can you say clearly the reasons

• 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 8 months ago

Amazing explanation step by step.

• Vikas Kumar 8 months ago +1

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

• 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 8 months ago +1

YOU SAVED ME FROM FAILING MATH TYSM

• NØ ØNE 8 months ago +1

You're the BEST

• Joy Lee Moorndoz 8 months ago

This is great!.

• 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 8 months ago

Thanks

• 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 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 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 9 months ago +10

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