# 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 CastroDay agoI have a test today I’m this is an hour

Gilma Ferrer2 days agoJG, you are the best, thank you for doing this!

RADO5 days ago^{+1}Math means mental abuse to humans

Jonathan Villa6 days ago^{+17}Who else is here because their discrete math professor can not explain this stuff well?

Ellie Mandy2 days agoJonathan Villa sweet, i go to Georgia Gwinnett College.

Jonathan Villa2 days ago^{+1}Ellie Mandy I go to Lewis University In Illinois!

Ellie Mandy2 days ago^{+1}hahaha me! what college do you go to?

Mark G05!8 days ago3:45 I still don't understand why did you choose four

Victor Harris10 days ago^{+2}I came here because I fell asleep while my teacher discusses this one

Torment10 days agogreat examples. where are more of proof type problems in your channel?

Jp Tayco11 days agoyou're better to teach than our teacher which is we paying her for lessons

Peyton Butler12 days agoliterally want to cry you saved my ass thank you

A7md_XgamZ13 days ago^{+1}I didn’t understand any of this . I spend a year to understand induction but I couldn’t 😩😩😩😩😩😩 FUCK IT

Ahmed Ismail16 days agoi just found heaven here

Aimee Finlayson23 days ago12.39 what happens to the (k+1)^3 it just disappears

DeviousShadows19 days agoHe factorized out the (k+1)^2. 4(k+1)^3 / (k+1)^2 = 4(k+1)

Aprishiela Hartono27 days agowhat a crystal clear explanation. Thank you very much :)

illlanoize2329 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 Lysenko29 days agoAs 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.

illlanoize2329 days agoU better have

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

migs sants29 days agoIt 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 FayeMonth ago^{+1}Our precalculus teacher taught that we needed to add the lcd to both sides

Ace GoMonth agoYou are always a savior.

Elijah BlakeMonth ago^{+1}Here you are saving the day again. Just like the last two years of my math classes.

Rodney MuganziMonth agoI love this dude

Bahar OsmanMonth agoMath induction is meaningless i hate it so much!!!!!!

Stephanie SotoMonth 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 DorolMonth agoSuper effective neto💖

Ab Abdi2 months ago^{+1}dont get how u expanded on 13:12

megha tirkey2 months ago^{+1}Can you please make a video on complex functions

major2 colonel2 months agoWOW i understood in no time great job mr tutor

Zachary Tabz2 months ago^{+10}"what still searching for math help? are videos from 2007 really help you?"jajaja lol

Gabriel idowu2 months agothanks so much for helping me out

Eniola Adejumo2 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. Abduba3 months agoVery helpful video......Thanks man

MALUMI Blessing Aderinke3 months ago^{+1}This made my day after struggling with this on my own...

luis soto3 months agothanks to your videos I passed my math classes

MALUMI Blessing Aderinke3 months agoluis soto congratulations

I hope to pass mine too

stellus francis3 months agoSo.. Can we add 4 to both the sides?? Or can we add whatever no that is given...?? There isn't any problem ryt? !!

Tin A4 months agoThanks man you're a lifesaver

Lexer Guevara4 months agowhat app are you using sir thankss

Lexer Guevara4 months agothankss sir

anuradha ramji4 months ago^{+6}Simple and easy explanation.Thanks to people like you ,maths is still interesting..praise God

Obada Zerkly4 months agothanks

The Geek Site5 months agoWhat is the use of this thing ?

Threelly AI5 months agoSo hyped...

chrome.google.com/webstore/detail/threelly-ai-for-youtube/dfohlnjmjiipcppekkbhbabjbnikkibo

Daniel Adewunmi5 months agoThanks you help me a lot

Rk Shuvo Raj6 months agoThank u sir

mishlol1236 months ago^{+1}okay you deserve a sub bro

this helped me alot

thank you very much

Moaz El-sawaf6 months agoThanks sir

Eyad tube6 months agohello 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 Onyango7 months ago^{+1}fantastic explanation thank you so much

Feel Physics7 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 Boxenhorn2 months agothere is a difference between induction and mathematical induction

SunCityRick7 months agoAfter a number of youtube vids and books this video finally helped me intuitively understand induction, thanks!

kalpana varsha7 months agoCan you say clearly the reasons

Karen Boxenhorn2 months agomathematical 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).

NetworkRob8 months agoAmazing explanation step by step.

Vikas Kumar8 months ago^{+1}Thank u sir your explanation helped me a lot thank u so much😙😙😁

Cedrick Cruz8 months agoin 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 Byun8 months ago^{+1}YOU SAVED ME FROM FAILING MATH TYSM

NØ ØNE8 months ago^{+1}You're the BEST

Joy Lee Moorndoz8 months agoThis is great!.

Brittany Chan8 months agookay but like why is this theory/ how they replace the k value with the previous answer so smart?

Maimai Halid8 months agoThanks

BHD TV9 months agoAnd in 12:00 how did you subtract 2 from (k+1)³ to give (k+1)

Where did the ² come from?

Robert Baker9 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 TV9 months agoThe 3rd equation was😏 that's not even how the law of indices works🙄... But thanks bro I never understood mathematical induction until today

Naman Chandra Srivastava2 months agoBro what do u mean

Zaheer Ahmed9 months ago^{+10}Thanks man I pass my discrete Math class because of you . you make things very clear and easy to understand