Mathematical Induction Practice Problems
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- เผยแพร่เมื่อ 30 ก.ย. 2024
- 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.
Intro to Statistics:
• Introduction to Statis...
Probability - Basic Intro:
• Introduction to Probab...
Binomial Theorem:
• Binomial Theorem Expan...
Permutations and Combinations:
• Permutations and Combi...
Factorials Explained!
• Factorials Explained!
__________________________________
Parametric Equations:
• Parametric Equations I...
Ellipses - Conic Sections:
• Writing Equations of E...
Hyperbolas - Conic Sections:
• Hyperbolas - Conic Sec...
Parabolas - Conic Sections:
• Finding The Focus and ...
__________________________________
Arithmetic Sequences:
• Arithmetic Sequences a...
Geometric Sequences:
• Geometric Series and G...
The Fibonacci Sequence:
• Mathematics - Fibonacc...
Mathematical Induction:
• Mathematical Induction...
Induction Divisibility:
• Induction Divisibility
__________________________________
Final Exams and Video Playlists:
www.video-tuto...
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Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
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Thank you so much
Who else is here because their discrete math professor can not explain this stuff well?
hahaha me! what college do you go to?
Ellie Mandy I go to Lewis University In Illinois!
Jonathan Villa sweet, i go to Georgia Gwinnett College.
lmao same
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your videos really helped me learn, mathematical induction, functions, logs, standard deviation, compound interest, arithmetic sequences, electromagnetic fields, electric fields, circuit, electricty physic stuff, geometric sequences, binomial expansions, factor theorem, remainder theorem, enthalpy change calculations, statistics, and some more stuff in this span of a week for all my exams since I was hospitalized and couldnt get out of bed I WAS REALLY BEHIND but I have managed to catch up an entire semester in a week or two thanks to you.
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look@ Jerryco Jauregue's videos on math induction, he pretty good job of explaining this stuff.
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i have been trying to teach myself induction all semester based of my professors notes. I havent made any progress. Finally I decided to look to youtube to help understand induction before i try to practice it. your video was beyond helpful and now i feel i have a much better understanding on induction. Thank you for the great video!
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holy shit what a good tutorial. i watched 4 videos on this and was so confused your explanations are so intuitive.
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hi, on 13:06. when u * 4 to both sides. why does (4k+1) ^3 been remove?
Everyone's ignoring that huh
Because we were doing a factorization, it’s correct as written. Now, if you're still confused, perhaps you just overlooked the (k+1) term inside the right bracket after the factorization.
After factoring out (k+1)^2 , the second term (k+1)^3 leaves behind just (k+1) inside the right bracket.
Because (k+1)² was factored from (k+1)³ which results in (k+1). Your misunderstanding stems from the fact you conjoined 4 with k when it should be 4(k+1)³. Hope this helps for you and for future students here :))
@@CG119Animatortoo bad we’re late, this comment was 3 yrs ago
honestly teachers should just play your videos in class instead of teaching it themselves, majority would get better grades
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Looking at this video before my final because I’m expecting having to do an induction proof, thanks for making it very clear
How did it go lol
Same lol
Final in 30 minutes!
@@ThePyroMEGA nice explanation,my textbook couldn't elucidate it this way for me
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At 11:56, why is the cube from 4(k+1)^3 removed?
because we factored by K+1
Because we were doing a factorization, it’s correct as written. Now, if you're still confused, perhaps you just overlooked the (k+1) term inside the right bracket after the factorization.
After factoring out (k+1)^2 , the second term (k+1)^3 leaves behind just (k+1) inside the right bracket.
i'm in shock bcuz i could never complete even a single simple induction exercise before watching you and now i just did. you taught me more in less than 20min than my teachers in 4 months
That bcz you didn’t listen your teacher carefully and not want to 😅
@@explorerendeavour3009 no? stop talking without knowing what goes in my life. we didn't have classes this was during COVID so we DIDN'T have classes, we had prerecorded videos that didn't explain anything in depth and we had to teach ourselves the best way we could. think before you talk.
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Yes he explains very well concept you know
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I didn’t understand any of this . I spend a year to understand induction but I couldn’t 😩😩😩😩😩😩 FUCK IT
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
I feel so happy and proud of myself for solving a proof on my own after watching your video ❤️❤️❤️❤️❤️ I thought I'd never do it
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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
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5:11 how do you distribute it . I don't know what he just did to make it like that
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I came here because I fell asleep while my teacher discusses this one
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Can you please tell me is there any workbook with problems so I can practice. btw nice video.
This is one thing that I “learned” in college algebra that I feel is going to come back and haunt me.
For the last problem I did:
Add 1 to both sides
1+ (2^n - 1 + 2^n )= 1 + (2^(n+1) - 1)
2^n + 2^n = 2^(n+1)
Simpify RHS:
2^n + 2^n = 2(2^n)
Factor out 2^n
2^n(1 + 1) = 2^n(2)
Simplify:
2^n(2) = 2^n(2) //
Is this correct?
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ive been trying to solve mathematical induction for days thank god ive found ur videos i could solve it within minutes now thank u so much u help me a lot xxx
sorry in advance, im really dumb
so i just want to clarify something since i was confused. at 3:34 why do u have to add the next term??? i thought 4k-1 was already the formula for the next term?
May be because I've seen a hundred other videos on the same topic but... this one finally hit. Thank you.
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At 11:53 of the video can anyone explain to me how he just removed the cube power from (k+1)^3 and change it into [k^2+4(k+1)]
someone should please reply this
He factored out a (k+1)^2 out of the entire first numerator. That left him with(k+1)^2 and then k^2 +4(k+1) because he took a square from a cube. Think of it as (K+1)^3 - (k+1)^2= k+1
He factor
This made my day after struggling with this on my own...
I really don't understand about the exponent 3 in the second problem in the left side of the equation on how it "disappear" in the next line :''( please enlighten me. And why does it regroups?
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thank you so much for making this video! may I suggest you to make a video about proving inequality using mathematical induction?
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Got 2 hours of sleep. I’m normally a math wiz, I’ve gotten a 100 on every exam this semester, but I’m finding myself being dazed and confused in the middle of a question. This causes me to want to start over. I’ve been stuck on Q1 for 3 hours now. Going to take a nap brb.
Where did u get the last part of K version like 2k square from and 4 K from can u explain those part please
basically imagine (k+1) is x and factor it out like a quadratic
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U understood?
After a number of youtube vids and books this video finally helped me intuitively understand induction, thanks!
!!!!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.
there is a difference between induction and mathematical induction
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Our teacher said that we should never change the right side we're only allowed to change the left... I don't get it.
you arent a llowed to move things over from the equal sign
Hahaha the 3rd equation seemed like u broke a million maths rules... (Aka.I am roo dumb to understand)
This short video helped me brush up my memory. Now I am ready for my class.
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You've been of great help! your videos are more lucid than our professor's hours of teaching honestly
Hey sir, plz plz plz tell about this question ,if I check it for p(1),it shows 3,according to which the 1 is 0th term and 2 is 1th term ,but 0 is not a natural number. Plz Tell me- 1+2+2^2+.........+2^n= 2^(n+1)-1 for every natural number
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