Discrete Math - 5.1.1 Proof Using Mathematical Induction - Summation Formulae

  Рет қаралды 131,776

Kimberly Brehm

Kimberly Brehm

Күн бұрын

Пікірлер: 56
@kletap4463
@kletap4463 4 жыл бұрын
I have been watching your videos all semester, you teach so well and clearly as opposed to my actual discrete math teacher. Thank you thank you so much for these videos
@detroitpistonsplayoffs
@detroitpistonsplayoffs 2 жыл бұрын
Utd?
@cybergamer__
@cybergamer__ Жыл бұрын
@@detroitpistonsplayoffs Utd student here! Same opinion as him😆
@detroitpistonsplayoffs
@detroitpistonsplayoffs Жыл бұрын
@@cybergamer__ let me guess, ntafos?
@cybergamer__
@cybergamer__ Жыл бұрын
@@detroitpistonsplayoffs nah, it's Ouyang
@heralds3164
@heralds3164 Жыл бұрын
You have no idea how much this video has helped me. I was stressing out about doing Mathematical Induction cuz my professor just flew thru the examples in class. Especially with the fact of trying to figure what I must prove and our proof paper is on mathematical induction. But with this video and the rest of the videos, it makes so much sense! I can finally go and do the proof paper with confidence! Thank you so much! I wish there were more teachers like you!!!
@brandon_b7459
@brandon_b7459 3 ай бұрын
As always, your videos are a godsend. I have felt so lost in discrete math, but your videos ALWAYS break it down in an 'easy-to-digest' way. I always come away from your videos understanding better
@robdunsmuir8090
@robdunsmuir8090 2 жыл бұрын
I am so thankful I found you. I've been struggling terribly with my university math course. Your videos are so well done, the explanations are clear and the video goes at a perfect pace. Thank you for giving me the confidence I need to continue. I'm taking it distance ed and it's impossible without actual explaining and examples
@mr.yousifkhan7724
@mr.yousifkhan7724 2 жыл бұрын
then why don't you attend your class
@robdunsmuir8090
@robdunsmuir8090 2 жыл бұрын
@@mr.yousifkhan7724 the university attend is 400 miles away and I’m taking the classes distance education. That’s how the entire courses offered.
@pandaonsteroids5154
@pandaonsteroids5154 Жыл бұрын
My professor does show that step! He is actually a great professor. I am a CS major so we take Mathematical Structures or Discrete Math for CS. Your videos are great for review before a quiz or test! Better than looking at my notes.
@pandaonsteroids5154
@pandaonsteroids5154 Жыл бұрын
The hardest part is the algebra 😂😂😭😭😭
@waleedmnaeem9946
@waleedmnaeem9946 3 жыл бұрын
disliker = the instructor who don't show the moooost important step in his video 😂😂😂
@ToxicOsOk
@ToxicOsOk 10 ай бұрын
At 21:19, shouldn't it be show that 1+3+5+...+(2k-1) + (2(k+1)-1) = (k+1)^2? Wait, nevermind... 2(k+1)-1 simplifies to 2k+2-1 = 2k+1 which is what you have.
@RafidShuvo
@RafidShuvo 10 ай бұрын
You taught a great way thank you ❤and your voice is also sweet
@HolyShadowNow
@HolyShadowNow 4 жыл бұрын
I wanted to ask why you added +2 (instead of +1) at 21:13, but then realised its because we have a set of only positive integers, and that is why we had to skip 0?
@SawFinMath
@SawFinMath 4 жыл бұрын
I added 2 because on the left side of the equation, we started at 1 and each subsequent value increased by 2, so 1, 3, 5...n, n+2, n+4, etc.
@HolyShadowNow
@HolyShadowNow 4 жыл бұрын
@@SawFinMath totally missed that, thank you for explaining!
@albertd.bangura3794
@albertd.bangura3794 3 жыл бұрын
@@SawFinMath Thanks mam for answering, you saved me from this same confusion.
@YuPois8520
@YuPois8520 3 жыл бұрын
how did you get (k+1)^2 21:27 ?
@semdinakt
@semdinakt 3 жыл бұрын
Because this is for S(k+1). The rule says S(k+1) : (k+1)^2
@boredguy5805
@boredguy5805 3 жыл бұрын
@@semdinakt what rule?
@SuzyZou1995
@SuzyZou1995 2 жыл бұрын
Such a great video, Thank you so much for the amazing explanation!
@mr.yousifkhan7724
@mr.yousifkhan7724 2 жыл бұрын
chup bhadwi
@ernestessel5941
@ernestessel5941 2 жыл бұрын
Great work!
@loveleaf5418
@loveleaf5418 2 жыл бұрын
Thank you so much for this video!!!!
@jeremiahbarro330
@jeremiahbarro330 Жыл бұрын
At 14:10 you say that we have to add to both sides to be mathematically correct, but we didn't do that in the proof just prior. Also, this proof works without adding to both sides because We want to show that 2^(k+1) - 1 + 2^(k+1) = 2^(k+2) - 1 2^(k+1) - 1 + 2^(k+1) = 2 * 2^(k+1) -1 by simple algebra = 2^1 * 2^(k+1) -1 by exponent rules = 2^(k+1+1) -1 = 2^(k+2) - 1 which is equivalent to the right side. This raises the question, when DO we need to add to both sides to be mathematically correct? Is it ever necessary or is it just another tool to be used for any equation?
@humnaazhar1662
@humnaazhar1662 Жыл бұрын
why is there a 1 there at 6:42?
@drewprof
@drewprof 3 жыл бұрын
Excellent work Kim.
@g_kub
@g_kub Жыл бұрын
saving my life
@samkelly5277
@samkelly5277 Жыл бұрын
In the proof of the summation formula, how do you know the base case is 1 if there is no parameter indicating the domain of n? Are we just to assume it's positive integers for all general proofs of formulas?
@SawFinMath
@SawFinMath Жыл бұрын
Yes. I should have made the domain explicit but it’s all positive integers!
@Hopetobebetter
@Hopetobebetter 11 ай бұрын
will you ever do videos on chapters like 5.1.4?
@SawFinMath
@SawFinMath 11 ай бұрын
Not for some time. My priority has to be for my own students, so I am working on content for them. Once that is complete I will be able to work on projects for my KZbin subscribers.
@Hopetobebetter
@Hopetobebetter 11 ай бұрын
@@SawFinMath understandable, thank you so much for your hard work!
@minh-tamvo4608
@minh-tamvo4608 2 жыл бұрын
You saved my life
@mannyw_
@mannyw_ 4 жыл бұрын
Would it be possible for you to label the videos with the chapter/lesson they're from? Thanks!
@SawFinMath
@SawFinMath 4 жыл бұрын
Yup. I did that and linked the full playlist, as well.
@dominicclark3774
@dominicclark3774 3 жыл бұрын
IIIIIIIIIIIjustCUSSED OMG. SO ******* CLEAR. It doesnt have to be hard lol, just use english and explanations. WOW.
@SawFinMath
@SawFinMath 3 жыл бұрын
Hah thanks! Glad I could clear it up for you!
@waifusaii
@waifusaii Жыл бұрын
Why did you stop at (k+1)(k+2)/2? I am not the best with algebra, but couldn't you have done more math? I just want to know when I should stop and move onto the next step.
@aarons7836
@aarons7836 Жыл бұрын
Thank you so much!
@oximas
@oximas 3 жыл бұрын
in the inductive hypothesis why do you use k and k+1 instead of n and n+1?
@SawFinMath
@SawFinMath 3 жыл бұрын
We are saying it is true for some random integer we are calling "k" and showing it is true for the next integer greater. It is a more general term than using n, which is already being used in our proof.
@AdriOPT
@AdriOPT 4 жыл бұрын
Thank you so much
@SawFinMath
@SawFinMath 4 жыл бұрын
No problem!
@miat789
@miat789 4 жыл бұрын
Oh man I am still struggling to understand why in the summation SHOW part we have k + k+1 on the left and then we substitute the ks with k+1 on the right.
@SawFinMath
@SawFinMath 4 жыл бұрын
Sorry I didn't get back to you sooner. We are adding the next value in the sequence on the left side, so 1+2+3...+k and then the next value would be k+1. On the right side, we need to show that the new sequence would be equivalent to f(k+1)
@RealestMFOnTheInternet
@RealestMFOnTheInternet Жыл бұрын
You are a god send
@bgxen23
@bgxen23 Жыл бұрын
i have my final tmr. Thank you
@fredphy1
@fredphy1 2 жыл бұрын
very good video
@alanpturing3362
@alanpturing3362 3 жыл бұрын
Thank you.
@zabiiaryan8325
@zabiiaryan8325 Жыл бұрын
🎉🎉❤❤
@elifwani
@elifwani 3 жыл бұрын
quick maths
@rachelvanderlely6324
@rachelvanderlely6324 3 жыл бұрын
@johnf367
@johnf367 3 жыл бұрын
Thank you so much
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