@@chandramohanr59 arre bhai 😂 haan sachchi, main dekhta tha when I was in 10th, now I'm about to pass 12th, and those days when I used to watch their lectures ❤️❤️ still miss them
Summary, :- we use “induction to prove a conjecture is true/not” In normal language, induction means *a method of discovering general rules and principles from particular facts and examples” The pattern of the foregoing proof until it’s true for one integer, then it shall be true for any other integer. Let P(n) be an assertion for a particular “n” First we prove if its true for n=1, “Base case” Then we see if it’s true for P(k), and prove it’s true for P(k+1) too. It’s like, a domino effect, where the assertion P(n) true for the first digit, n1, will lead it to be true for all the other integers. It’s like a generalisation of the formula over the integers.
Best teaching is used ❤️. It's really beautiful understandable to anyone who just know English. I love Don't memorise It helps me to understand many things and open my mind toward next level understanding.
Thank you this is God's blessing I was praying for help and im on the last question of a quiz that literally took me all day from 12 am to 8 pm and i go to this video and my question the last one i am on is 2 + 4 + 6 + ... + 2n = n(n + 1) THANKS!
well, i'm indonesian and math is the subject that i hate so much. im not hate it's knowledge, but i hate when school "force" me to understand them in such a uneffective ways. thanks to that, now i used to watch abroad explanation rather than from my country, luckily i can take english a little bit.
Miss, on the left-hand side, it was 2+4+6+....+2k. And when you explain k+1 part you actually write 2+4+6+....+2k+2(k+1) instead of just replacing 2k with 2(k+1). Why is it? It is easy to understand that you replace k with k+1 on the right-hand side but instead of replacing you have added an extra 2(k+1) to the left-hand side. For me it is confusing and I do not understand it. Can you explain this if you understood what I meant?
Same thing bro. I'm watching the comments trying to understand how everyone missed that. Where the hell did that extra 2(k+1) come from ?! driving me nuts man
@@wakajeng It was actually 6 months ago when I asked this question but it is not unclear for me anymore. While the concept might seem straightforward, it can be a bit tricky at first. Let me clarify it for you. When we use induction, we first prove a base case, usually for the smallest possible value of n, which in this case is n = 1. For the base case, we verify that the statement (2+4+6+...+2k = k(k+1)) is true for n = 1. Then we assume that the statement is true for a general value of n, which we call n = k. Thus we assume that 2 + 4 + 6 + ... + 2k = k(k+1) is true. Now the next step is to show that if it holds for n = k, it also holds for the next value, n = k+1. To do this, we want to use our induction assumption (2 + 4 + 6 + ... + 2k = k(k+1)) on the first part of the left term, and then show that the last term (2(k+1)) gives us the desired result (k(k+1)). Therefore, we write the left term for n = k+1 as: 2 + 4 + 6 + ... + 2k + 2(k+1) And now we apply our induction assumption to the first part (2 + 4 + 6 + ... + 2k): 2 + 4 + 6 + ... + 2k = k(k+1) Now we have: k(k+1) + 2(k+1) And if we factor common terms: (k+1)(k+2) We have now shown that if the statement is true for n = k, it is also true for n = k+1. By showing that the base case (n = 1) is true and that the induction step works (if it holds for n = k it holds for n = k+1), we show that the statement (2 + 4 + 6 + ... + 2k = k(k+1)) is true for all natural numbers n. The important thing is that we keep two separate parts of the left term in order to use the induction assumption on the first part and then show that the last term gives us the desired result. Hope it is clear now 🙂
@@ennieguliyev ohhh i get it. so the extra 2(k+1) is there because it's the next term after 2k. i think they should have included that in the video as well (even though it may sound straightforward in retrospect, a lot of us aren't good at maths to begin with 😅)
If you have a conditional statement and the antecedent is false (x is fire), then the statement is always true (this is because a conditional statement is only false when when the antecedent is true and the consequent is false). So, in this video, when you use ice and fire as the antecedents, are you using first-order predicate logic ? Something else ? In all of the discrete math or data structure textbooks I have looked at, there is always an introduction to first-order predicate logic and then mathematical induction, and I am assuming that mathematical induction uses first-order predicate logic. So, maybe the video in this section should just focus on how if ice is true, the implication cannot be false if the consequent is also true. And in mathematical induction, the truth of the consequent is the proof that is performed (using the true antecedent) I think it is important not to confuse an implication statement with a statement of causation. I am still learning in the field and would be open to correction on this matter.
At 4:03 you said that P(1)R.h.s=1(1+1)=2 But mam I think it's don't give the first term...it gives the sum of first term which is 2 itself... Sum of 1st two terms will P(2)=2(2+1)=6 Sum of 1st three terms P(3)=3(3+1)=12 Mam please reply me so that I can clear my concept
You're most welcome. We are glad that you understood the concept. We are happy that we could help you learn. You motivate us to do better. Keep watching our videos : )
What is exactly the principle of mathematical induction? Definition please Though , I understood the video completely( and it was great ) I couldn’t grasp on a concept
I think you forgot to add the first term to the LHS of the equation. For when the expression has 2 terms, we have P(2) = 2 + 4 = 2(2 + 1) equal to 6 = 6 which is correct.
At 5:15 it was taken in the video as below: GOAL: to prove for RHS P(k+1)=k(k+1) But I PRESUME that statement to be: P(k+1)=n(n+1)---->according to the formula which was mentioned at the beginning (0:38) So, now substitute: n as (k+1)---->because we are trying to prove for P(k+1). The following steps are: P(k+1)=(k+1)[(k+1)+1] =(k+1)(k+2) Therefore, LHS(which was proved before, from 4:44 to 5:15) is equal to RHS(which is now proved) Hope You understood it. If I had mistaken something, reply me.
It goes like this. You first prove that it works for 1. Then you prove that it works for any natural no k + 1 if it works for k. Now we have shown that it works for 1. Taking that as k, it also has to work for k+1 which is 1+1=2. Now you take 2 as k. Then it also holds for k+1=2+1=3. Now you take 3 as k. So it should also work for 4. Like this you can prove that it works for any natural no. Hope this helped!
@@Karan-un8uz Bro don't get depressed , we all have our weak points , the important thing is to not give up , watch again you will surely understand...
@@yashdukhande9013 Hi bro , now I am in grade 10 , I want to give the JEE exam so I want to learn some advanced topics , I have learnt vectors , 11th grade Calculus and Kinematics up until now .
@@golumandal4836 If you go to college, make sure it's worth the money because the workload is way lighter and they basically go over these topics in the worst possible way. TH-cam is definitely outperforming colleges by a long shot.
I am eagerly waiting for the day when the number of subscribers would reach 1M
Americans are too busy watching "the game". I don't know about other countries.
Well, the day has come indeed.
the day has come
Aaj khush toh bohot hoge tum
@@chandramohanr59 arre bhai 😂 haan sachchi, main dekhta tha when I was in 10th, now I'm about to pass 12th, and those days when I used to watch their lectures ❤️❤️ still miss them
Explanation was clear and concise. You are a wonderful teacher!
Thank you so much.
I'm here ,when my teacher failed to explain me this concept in a better way
But u truely nailed it ,finally understood 😊😊
What year are you???
why are you talking shit behind my back? You should ask me directly at our class instead of posting here that I failed you.
@@sirianfreyra9832 who r u .....
I know u not
@@sirianfreyra9832 oh crud
Summary, :- we use “induction to prove a conjecture is true/not”
In normal language, induction means *a method of discovering general rules and principles from particular facts and examples”
The pattern of the foregoing proof until it’s true for one integer, then it shall be true for any other integer.
Let P(n) be an assertion for a particular “n”
First we prove if its true for n=1, “Base case”
Then we see if it’s true for P(k), and prove it’s true for P(k+1) too.
It’s like, a domino effect, where the assertion P(n) true for the first digit, n1, will lead it to be true for all the other integers. It’s like a generalisation of the formula over the integers.
Best teaching is used ❤️.
It's really beautiful understandable to anyone who just know English.
I love Don't memorise
It helps me to understand many things and open my mind toward next level understanding.
U r better than any e - learning media.... really👍👍👍
India is proud to have this you tube channel.
Really true
One of the best channels I found on TH-cam. Happy for learning this vast chapter in a few minutes!
Thank you very much for the video. Tomorrow is my maths exam which includes this topic also And the notif. just came on the right time. THANK YOU.
You have a great skill in teaching❤
I Deduced 'em😂❤
Never thought i would see you here
@@agbluemetal2364 You're in the cycle rn. You'll go through all the videos I went through a year back.
@@teratrox4685 🙂
Thank you this is God's blessing I was praying for help and im on the last question of a quiz that literally took me all day from 12 am to 8 pm and i go to this video and my question the last one i am on is 2 + 4 + 6 + ... + 2n = n(n + 1) THANKS!
Really?
@@lifeisbeautiful1562 yea no joke
@@thehoboeskimo9888 how was your quiz then?
@@lifeisbeautiful1562 idk yet it was teacher graded but from what I learned from the lesson and videos i did i think i did great
@@thehoboeskimo9888 Good then.
Stay safe.
You explained this to me in 6 minutes better than my professor in a 1 hour class, thank you for this video
u deserve more like and love madam. My respect from Ethiopia
Thank You Madam .. i have seen many others video but could not understand , by this video I understand completely..
thank you.
Short duration. Well explained. Loved it 😊
The great teacher I have ever met on TH-cam ! Thank u so much ♥
I HOPE YOU MAKE UR PREMIUM VERSION FREE TO ANYONE. POOR STUDENTS LIKE US RELY ON TH-camRS LIKE YOU FOR CONCEPT DEPTH.
Please upload videos on biotechnology and molecular basis of inheritance
Your videos on genetics and calculus were superrrrrb
How can we assume P(k) is true in inductive hypothesis? Isn't it the whole this we are trying to prove?
You all are doing very good for all of us...
Your teaching method is awesome.
Glad you think so Musab. We are glad that you understood the concept. For more videos, please visit our website - dontmemorise.com/
Thank you so much, you have helped me prodigeously💐💐
well, i'm indonesian and math is the subject that i hate so much.
im not hate it's knowledge, but i hate when school "force" me to understand them in such a uneffective ways.
thanks to that, now i used to watch abroad explanation rather than from my country, luckily i can take english a little bit.
Mashallah. To be honest it was an amazing lecture. From start to end all of my concepts got clear. May Allah Almighty bless you. Aameen
Solve this please
Find the value of x and y if
-3x+(2y)i-xi+5y=7+5i,under complex numbers
if You have asked the valu(e) of X and Y , then two we can't get values from a single equation
Awesome 👍
Thank you, Keteshwari!
We hope you had a great learning experience 😊
Yuppp
Miss, on the left-hand side, it was 2+4+6+....+2k. And when you explain k+1 part you actually write 2+4+6+....+2k+2(k+1) instead of just replacing 2k with 2(k+1).
Why is it? It is easy to understand that you replace k with k+1 on the right-hand side but instead of replacing you have added an extra 2(k+1) to the left-hand side.
For me it is confusing and I do not understand it. Can you explain this if you understood what I meant?
Same thing bro. I'm watching the comments trying to understand how everyone missed that. Where the hell did that extra 2(k+1) come from ?! driving me nuts man
@@wakajeng It was actually 6 months ago when I asked this question but it is not unclear for me anymore. While the concept might seem straightforward, it can be a bit tricky at first. Let me clarify it for you.
When we use induction, we first prove a base case, usually for the smallest possible value of n, which in this case is n = 1. For the base case, we verify that the statement (2+4+6+...+2k = k(k+1)) is true for n = 1.
Then we assume that the statement is true for a general value of n, which we call n = k. Thus we assume that 2 + 4 + 6 + ... + 2k = k(k+1) is true.
Now the next step is to show that if it holds for n = k, it also holds for the next value, n = k+1. To do this, we want to use our induction assumption (2 + 4 + 6 + ... + 2k = k(k+1)) on the first part of the left term, and then show that the last term (2(k+1)) gives us the desired result (k(k+1)).
Therefore, we write the left term for n = k+1 as:
2 + 4 + 6 + ... + 2k + 2(k+1)
And now we apply our induction assumption to the first part (2 + 4 + 6 + ... + 2k):
2 + 4 + 6 + ... + 2k = k(k+1)
Now we have:
k(k+1) + 2(k+1)
And if we factor common terms:
(k+1)(k+2)
We have now shown that if the statement is true for n = k, it is also true for n = k+1.
By showing that the base case (n = 1) is true and that the induction step works (if it holds for n = k it holds for n = k+1), we show that the statement (2 + 4 + 6 + ... + 2k = k(k+1)) is true for all natural numbers n.
The important thing is that we keep two separate parts of the left term in order to use the induction assumption on the first part and then show that the last term gives us the desired result. Hope it is clear now 🙂
@@wakajeng bro me too I literally got the whole video except why the last terms comin from??? kinda regretting taking math
@@wakajeng
Take last 2 term of that series
2(n-1) + 2n
Now put n = k+1
You will get 2(k+1-1) + 2(k+1)
2k +2(k+1) 🤗
@@ennieguliyev ohhh i get it. so the extra 2(k+1) is there because it's the next term after 2k. i think they should have included that in the video as well (even though it may sound straightforward in retrospect, a lot of us aren't good at maths to begin with 😅)
Thank you Soo much ☺️ really it is very easy after seeing this video 🤗🤗
Super explanation thank u so much
This lady is an educational genius despite having an accent that is difficult to listen to.
It may be b'coz you possess a different accent
Well explained . It looked difficult but you taught in very simple example
This is such a good video. If only I wasn't 5 years younger than the age you are supposed to learn this.
Thanks a lot, Fareeha!
Glad you liked our video.
Keep watching! 🙂🙂
Please make video for FOURIER SERIES with example and tricks.... 👍
I easylly understood the concept from this vidio.thanks🖐✍👊👮♂️👨💻
Nice explanation as always thankyou so much
You're very welcome! :)
Plz add a video on phase contrast microscope
If you have a conditional statement and the antecedent is false (x is fire), then the statement is always true (this is because a conditional statement is only false when when the antecedent is true and the consequent is false). So, in this video, when you use ice and fire as the antecedents, are you using first-order predicate logic ? Something else ? In all of the discrete math or data structure textbooks I have looked at, there is always an introduction to first-order predicate logic and then mathematical induction, and I am assuming that mathematical induction uses first-order predicate logic. So, maybe the video in this section should just focus on how if ice is true, the implication cannot be false if the consequent is also true. And in mathematical induction, the truth of the consequent is the proof that is performed (using the true antecedent) I think it is important not to confuse an implication statement with a statement of causation. I am still learning in the field and would be open to correction on this matter.
At 4:03 you said that P(1)R.h.s=1(1+1)=2
But mam I think it's don't give the first term...it gives the sum of first term which is 2 itself...
Sum of 1st two terms will
P(2)=2(2+1)=6
Sum of 1st three terms
P(3)=3(3+1)=12
Mam please reply me so that I can clear my concept
I'm sorry could you frame ur question better? I could clear it but ur doubt is not so clear
Outstanding 👍🏼👍🏼👍🏼👏👏👏
Such an underrated channel
guys plz make more videos on 11th class maths topics.thank u
Thank you 🙏🙏
Finally I understood this concept 😀
Mam you are proving lhs =rhs but before proving how did you concluded or derive such formula......n(n+1)please tell me mam
It's the equation for finding sum of an arithmetic sequence.
Just curios, why we chose K + 1 as our assumption?
I mean what about K + 2 will it still work?
Thanks a lot, greetings from Brazil!
You're most welcome. We are glad that you understood the concept. We are happy that we could help you learn. You motivate us to do better. Keep watching our videos : )
this lesson is really difficult to me.... but you the best at explaining this stuff to me, I really appreciate your video!
Nice explanation...well done
Just wow. You have truly hit on something awesome here. Concepts broken down into digestible parts. Bravo.
Congratulations for 2 million
What is exactly the principle of mathematical induction?
Definition please
Though , I understood the video completely( and it was great ) I couldn’t grasp on a concept
Please for the last Part of the Right hand side where it was = k+1([k+1]+1)
How did she arrive at
(K+1)(k+2)
Very nice explanation. Making Math learning easy..
Thanks a lot ...
Thank you
Thankyou
Wow!
Thank you Mm
Thanks a lot
How can we related the process of RHS with k+1, with the domino example? It should have mentioned clearly at the end.
This is spectacular! Thanks for creating.
4:52
how that 2k came in P of k + 1?
I don't see how 4=n(n+1). In this case, isn't n equal to 2? 2(2+1)=6, not 4.
I think you forgot to add the first term to the LHS of the equation.
For when the expression has 2 terms, we have P(2) = 2 + 4 = 2(2 + 1) equal to 6 = 6 which is correct.
n = number of terms which in this case is 2
So
2+4 = 6 LHS
2(2+1) = 2(3) = 6 RHS
since LHS = RHS
hence proved
Order of operations (bodmas)
Which software do u use for explaining maths
At 5:25 how do we get +1 extra in the second term
(k+2) = (k+1+1) 🤗
Thank you very much mam😊
You are most welcome, Katie. We are glad we could help you out😊
Thank you very much
Really helpful
If x is water
Is it cold water or hot water
Will you please explain coordinate geometry pls
U are the best
Why are we repeating'k' when n=k+1 ?
@dontmemorise ?
Good explanation mam thanks
Thanks
how did the k(k+1) become 2(k+1)?
Please in the RHS of the problem where did the last +1 in (k+1)[(k+1)+1] come from?
Simply put k=k+1 it will be =k(k+1)
(K+1)(k+1)+1)
But at 4:52 I can't get it the 2(k+1)
Helpful😺😺😺😺😺😺😺😺
Thank you so much 💕
Naruto
the link of dont memorise consists of an apostrophe and hence does not work
I deduced that (;
Finally understood...
Amazing explanation
I got lost at 4:46 . What happened to the expression? where did 2(k+1) come from?
Bro as we write 2k ,the next term should be 2(k+1) as explained in Domino effect
what she said 3:12?
What program do you use?
I know mathmatics but i don't know how to create a video like this please help me
Try Latex
How do you get the answer for the RHS of condition 2 from k(k+1) to (k+1)(k+2). Please simplify
At 5:15 it was taken in the video as below:
GOAL: to prove for RHS
P(k+1)=k(k+1)
But I PRESUME that statement to be:
P(k+1)=n(n+1)---->according to the formula which was mentioned at the beginning (0:38)
So, now substitute: n as (k+1)---->because we are trying to prove for P(k+1).
The following steps are:
P(k+1)=(k+1)[(k+1)+1]
=(k+1)(k+2)
Therefore, LHS(which was proved before, from 4:44 to 5:15) is equal to RHS(which is now proved)
Hope You understood it.
If I had mistaken something, reply me.
@@varshinilolla3090 I'm sorry I can't understand it either
@@Alyssa_1306 Oh! I will try to simplify it once again.
@@varshinilolla3090 oh I finally understood
Thank you
I need an explanation video for Cauchy induction
Awesome mam❤️
Thank you, Anjum!
Keep watching! 🙂🙂
Can i ask madamm? How do you make a mathematical statement?
i am the first viewer of this video ...☺☺
Does it mean that the formula presented in the right hand side is true logically but not always realistically true? I'm such a slow learner.
All formulas are universally Verified, you can find Exception in Physics but not in Maths
It goes like this. You first prove that it works for 1. Then you prove that it works for any natural no k + 1 if it works for k. Now we have shown that it works for 1. Taking that as k, it also has to work for k+1 which is 1+1=2. Now you take 2 as k. Then it also holds for k+1=2+1=3. Now you take 3 as k. So it should also work for 4. Like this you can prove that it works for any natural no. Hope this helped!
The fact that I being in 9th can understand this , explains the quality of this video...
That fact that im in 11th and cant understand this video proves how stupid i am.
@@Karan-un8uz Bro don't get depressed , we all have our weak points , the important thing is to not give up , watch again you will surely understand...
Why are you seeing this video in the 9th grade ...there's better things to do.
@@yashdukhande9013 Hi bro , now I am in grade 10 , I want to give the JEE exam so I want to learn some advanced topics , I have learnt vectors , 11th grade Calculus and Kinematics up until now .
@@golumandal4836 If you go to college, make sure it's worth the money because the workload is way lighter and they basically go over these topics in the worst possible way. TH-cam is definitely outperforming colleges by a long shot.
By the way i m student of BS EDUCATION, and learned a lot about inductive and deductive reasoning, but not interested in mathematics 😏
what?
i still don't get the part from 4:45. can anyone explain ?
this is the first video of don't memorise, I didn't understand.
K(k+1)
How to solve
Am i the First Viewer 🤔🤔🙄
You entered this video because it is the shortest one among other mathematical induction videos.
Admit it.
Can you give a subtitle in indonesia ?😊
I was in the middle of the video and i was like i do not understand and I saw the title that says dont memorise and I
am like oohhhhhhhhhhhhhh
The domino comparison is far from apt, I feel.
Pointless, I have a test tomorrow and I learned nothing from this
Uhh so you find logical reasoning pointless?
maybe you shouldn't have waited until the day before a test to learn a subject 🙄