Sequences - Free Formula Sheet: bit.ly/4eau2KQ Arithmetic Sequences: kzbin.info/www/bejne/o6moenmFbduLgbs Geometric Sequences: kzbin.info/www/bejne/sHuoiJavqKaWapY Final Exams and Video Playlists: www.video-tutor.net/
@parthpopli64093 жыл бұрын
Bro this guys is definitely a polymath, genius
@ashy2683 жыл бұрын
I've got an exam 3 hours from now. Binge-watching your vids really helped me prep. Thank you sir, you're a legend!
@GHOST9411312 күн бұрын
Lol
@maarinahope4 ай бұрын
My lecture actually left us with this question of how to derive the formula. I didn't even know where to start 😢. You are a life saver . Thank you
@zahraashrafzade8948 Жыл бұрын
This way of learning math is what I do love. Thanks for the amazing teaching!
@utilizator17013 жыл бұрын
Nice demonstration of the sum formula of a geometric series. The only demonstration I have known before implies polynomial divison.
@SnehaSingh-44Ай бұрын
Amazing video, after watching so many of these, I've finally understood that sum of infinite series one! Thank you so much sir!
@zacharytapalgo36742 жыл бұрын
If u ever need help in math this guy will always pop up
@user-xu6ie9js9z23 күн бұрын
I couldn't make it to the class the day my teacher taught this the class. I have an exam in two days. Thanks for the video
@islamwaled5956 Жыл бұрын
11:50 Literally mind blowing You are amazing, man
@danielkim21063 жыл бұрын
Petition to buy this man a new mic
@aujiel62003 жыл бұрын
+1
@waltergnerre10 ай бұрын
1:00 minute of the video and I got the concept, thank you🙌🏼
@princekhadka54816 ай бұрын
I was stucked again and here is my saviour❤❤❤❤
@danicalauriquez43422 жыл бұрын
hello. Good day. Can I ask for permission from you to let use your video in my unit plan. For educational purposes only.
@user-dg6lo9fn8u8 ай бұрын
Thanks a lot!
@MuhammadUmer-ku3ye2 жыл бұрын
Why did you multiply sn with r??
@isaamvibez8913 Жыл бұрын
its a trick to increase the power of r of each term on the right side by 1, so now when u minus the two things the terms cancel out and ur left with only a few Sn = a + a^r +ar^2 + ar^3 ... ar^N-1 -r*Sn = a^r+ar^2+ar^4 ... ar^N when u add these both series u willl get Sn - r*Sn = a + a^r +ar^2 + ar^3 ... ar^N-1 - (a^r+ar^2+ar^4 ... ar^N) terms on the right cancel out and u are left with Sn(1-r) = a-ar^N Sn = a(1-r^N) / (1-r)
@youssofasiry72333 жыл бұрын
Could you please tell us witch program do you use for totirial.
@MathZoneKH3 жыл бұрын
Congratulations 🎈🍾 for more than 3M subs
@iaminthenowhereinn2 жыл бұрын
Hello, may I ask why r is multiplied to the series...?
@pawnhearts8785 Жыл бұрын
I’m guessing so that the n-1 exponent in the last term just becomes n.
@isaamvibez8913 Жыл бұрын
its a trick to increase the power of r of each term on the right side by 1, so now when u minus the two things the terms cancel out and ur left with only a few Sn = a + a^r +ar^2 + ar^3 ... ar^N-1 -r*Sn = a^r+ar^2+ar^4 ... ar^N when u add these both series u willl get Sn - r*Sn = a + a^r +ar^2 + ar^3 ... ar^N-1 - (a^r+ar^2+ar^4 ... ar^N) terms on the right cancel out and u are left with Sn(1-r) = a-ar^N Sn = a(1-r^N) / (1-r)
@zulawindsor57132 жыл бұрын
How we can find the Polynomial (Suppose it called P ) Where we find that function P is a composite of function P and P (PoP =P )🤯🤯??
@fadijabr8992 Жыл бұрын
Keep the good job.
@bhargavasaie39263 жыл бұрын
Thank you for posting It's very helpfull
@tanmaykulkarni15403 ай бұрын
14:05 what is |r|>1?
@bcolsant Жыл бұрын
At 9:44 why do you add the two equations? What do those last three steps represent?
@Soul-cu8zn Жыл бұрын
You can do whatever you want
@eugene1882 жыл бұрын
I get that the General Formula works, and how it is derived. but not sure why it is multiplied by r (or -r). Why did someone decide to then add the 2 formulas. The arthmetic series formula and how it is derived makes so much more sense.
@wyattdelaney-lefebvre1561 Жыл бұрын
I've been looking everywhere for an explanation for this
@gabble287 Жыл бұрын
@@wyattdelaney-lefebvre1561just started learning about this aswell and all the proofs I see jjst randomly throw in subtracting rSn from Sn. Did you ever find an answer to that?
@JulianGonzalez-ej2fi10 ай бұрын
This is so funny I was looking for the reason as well and every video I find they just do it without an explanation. And people just soak it up. I'm glad I'm not crazy
@TryagainMukanga7 ай бұрын
Multiplication by r and subtracting the resulting equation is a way to find Sn by elimination the same way we do when solving simultaneous equations.
@luanfigueiredo72833 ай бұрын
thanks
@AchinthaPallegedara8 ай бұрын
Thank you so much 😊
@malanhemal65742 жыл бұрын
what' s the reason it's multiplied by r?
@isaamvibez8913 Жыл бұрын
its a trick to increase the power of r of each term on the right side by 1, so now when u minus the two things the terms cancel out and ur left with only a few Sn = a + a^r +ar^2 + ar^3 ... ar^N-1 -r*Sn = a^r+ar^2+ar^4 ... ar^N when u add these both series u willl get Sn - r*Sn = a + a^r +ar^2 + ar^3 ... ar^N-1 - (a^r+ar^2+ar^4 ... ar^N) terms on the right cancel out and u are left with Sn(1-r) = a-ar^N Sn = a(1-r^N) / (1-r)
@Soul-cu8zn Жыл бұрын
Bro study some algebra
@malanhemal6574 Жыл бұрын
@@Soul-cu8zn Your comment was really helpful.
@Soul-cu8zn Жыл бұрын
@@malanhemal6574 good for you
@akshathbalak7 ай бұрын
*Why* do we minus rSn from Sn to get the formula. I don't have an intuitive understanding of it.
@dalisabe626 ай бұрын
It is one of those algebraic tricks that are used in mathematical proofs to derive a formula for something that is not too obvious to see. Herein, the infinite series is very difficult to see because it is infinite. So this is our algebraic manipulation to find the sum. It is genius and not every one could think about it.
@user-ts3xq3cy4f Жыл бұрын
Thank you
@nsuarez5 ай бұрын
Thank you!
@gulinasirova3257 Жыл бұрын
You are a legend !
@emmanueljangad11 ай бұрын
Thank you so much ❤
@bigred45922 жыл бұрын
what drawing software do you use?
@peterhindes56 Жыл бұрын
Probably Photoshop, but you can use anything like Krita
@happyfrezar28135 ай бұрын
Thanks man 🙏✊
@frankdenverellorquez819511 ай бұрын
Anyone knows what app is he using?
@milessodejana27542 жыл бұрын
why is r^n as n approaches infinity equal to 0?
@vandanasings2215 Жыл бұрын
Because 0< r
@inj19793 жыл бұрын
Thank you. 🌻
@AlexMwakacheya6 ай бұрын
I like this
@Niv_0503 жыл бұрын
super cool stuff ^.^ very interesting.
@bcolsant Жыл бұрын
At 8:33 WHY do you multiply both sides by r?
@youneedtocalmdown.8 ай бұрын
Convenience
@oliviacole10002 жыл бұрын
I was really confused as to why the series was multiplied by r. I found another video (and webpage) that explains this better, which I'll reply to this comment with in case the channel owner wants to delete it (I get it, I am techichally advertising another creator) so he doesnt delete my explanation too. !!(MY EXPLANATION IS IN THIS COMMENTS REPLIES)!!
@oliviacole10002 жыл бұрын
Basically, by multiplying by r, you "shifted over the summation, and got one more new term: r^n." This is important in the next step, because subtracting the two equations (rSn from Sn, or Sn-rSn) cancels out all but two terms: the a1, which was 'lost' when you multiplied Sn by r, and the new term from rSn, r^n. That leaves you with "Sn - rSn = a1-r^n". From there, it's what's said in the video: Isolate Sn. --->(factor Sn out on the left side, getting Sn(1-r), then---> factor a1 out of the left side, getting a(1-r^n), then---> divide both sides by (1-r) to get the final result Sn=(a(1-r^n))/(r-1). !! LOOK AT EDIT WHEN YOU READ THIS PART !! When looking up the formulas for the geometric sum formula, I was also really confused because there were a bunch of different versions of it, and nothing was very clear about why they were different, so here's a reminder: a((r^n-1)/(r-1)) = (a(r^n-1))/(r-1) because a is a/1, so you've just multiplied a out. Also: a((r^n-1)/(r^n-1)) = a((1-r^n)/(1-r)) because you're multiplying the fraction by -1/-1, meaning nothing is changing (the negatives cancel each other out, aka you're technically multiplying the fraction by 1). Just remember that both the numerator and the denominator have to be written the same, because -1/1 doesn't equal 1, and 1/-1 does not equal one. Edit: I just came across something on www.cuemath.com/geometric-sum-formula/ that says if |r|< 1, the sum formula for finite terms is a((1-r^n)/(1-r)), and if |r|>1, the sum formula for the finite terms is a((r^n-1)/(r^n-1)). If you can, I would ask your teacher/Tutor/anyone who is good with math about it.
@hirenmistry2085 Жыл бұрын
Good video
@luismillones25273 жыл бұрын
Genius!
@everyzylrian Жыл бұрын
thank u
@lordmomstealer3 жыл бұрын
Its like AP ( ARITHMETIC PROGRESSION )
@finthehuman65223 жыл бұрын
Did he remove some of his videos?
@emmanuelthorpe32153 жыл бұрын
One day I will be like you
@jeffreya.faulkner83672 жыл бұрын
Great, but for one little thing: you say "r sub n" when you mean "r raised to the power n," at the end of the video.
@ammarghaznavi46443 жыл бұрын
thx
@Carrymejane6 ай бұрын
11:20 😮
@theaveragesharma32748 ай бұрын
Sir you are so fucking cool I absolutely love your channel ❤❤❤