Finding The Sum of an Infinite Geometric Series

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  • Опубліковано 13 гру 2024

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  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +14

    Sequences - Free Formula Sheet: bit.ly/4eau2KQ
    Final Exams and Video Playlists: www.video-tutor.net/
    Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
    Arithmetic Sequences: ua-cam.com/video/mxEIFO8vXKY/v-deo.html
    Geometric Sequences: ua-cam.com/video/zJEWcysAc44/v-deo.html

  • @killallpikles3243
    @killallpikles3243 4 роки тому +773

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    • @zeyad7947
      @zeyad7947 3 роки тому +24

      i swear to God thats the same with me, even for physics and chemistry.... and especially math now, cuz these online lectures really be crappy as hell so at one point i just ditched the lectures and started watching this guy's videos instead, and i ended up with an A+ in Calc 1. this dude's great!

    • @thepeeps191
      @thepeeps191 3 роки тому +2

      Ikr

    • @frijolex2509
      @frijolex2509 3 роки тому +4

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    • @reignhard4696
      @reignhard4696 3 роки тому +2

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    @00_002 3 роки тому +404

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    • @dazllc
      @dazllc 2 роки тому +23

      you guys take this at university? im in 11th grade lmao

    • @00_002
      @00_002 2 роки тому +25

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    • @ezramantini8078
      @ezramantini8078 2 роки тому +5

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    • @mwu365
      @mwu365 2 роки тому +13

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    • @shoumodeepmukherjee8736
      @shoumodeepmukherjee8736 2 роки тому

      @@dazllc same bruh

  • @rexr3306
    @rexr3306 5 років тому +218

    I literally saw your first example and explanation and understood it right away while my trash math teacher spent 3 days in class trying it explain this and no one understood I saw your video and got it literally within the first 2 minutes. Why cant teachers teach in effective ways that are easy instead of the crappy traditional methods. Thank You!

    • @mullins69
      @mullins69 5 років тому +2

      15:39 how did he get e value

    • @daUrbanCyclist
      @daUrbanCyclist 5 років тому +15

      @@mullins69 Thats the universal value of *e* .Like pi has the value 3.1415 , e has the value 2.718

    • @Vin_03
      @Vin_03 4 роки тому +2

      Atleast your teacher described it but in my case only homework.

    • @1S0J1
      @1S0J1 4 роки тому +1

      same bruv.

    • @goodolnonamee
      @goodolnonamee 4 роки тому +8

      I know right, my dumbass teacher made it a million times more complicated than it had to be

  • @puppies3742
    @puppies3742 4 роки тому +65

    2 minutes in and you've taught me more than my calc prof and the textbook. I've read this chapter like 5 times and could not understand it. Thank you.

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    @sofia9189 2 роки тому +18

    I watched 2 minutes of this video and IMMEDIATELY understood something I've been trying to get for 2 weeks! Thank you so much!!!!

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    @R0el_syntax 5 днів тому +1

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    @chrispinchileshe8557 6 років тому +509

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    • @adityabhardwaj3495
      @adityabhardwaj3495 3 роки тому +17

      for real! I always watch his videos after my school and tuitions just to properly grasp the topic

    • @surelock3221
      @surelock3221 3 роки тому +33

      You're baked?

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      @KJ-rc6qs 3 роки тому +10

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      @dulxbe4883 3 роки тому +6

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    • @-clipz-
      @-clipz- Рік тому +1

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  • @silasj3412
    @silasj3412 5 років тому +209

    How did people understand this before Mar 28, 2018

    • @adityabhardwaj3495
      @adityabhardwaj3495 3 роки тому +3

      I wonder

    • @surelock3221
      @surelock3221 3 роки тому

      My grade 11 teacher did a pretty good job teaching this unit actually

    • @adityabhardwaj3495
      @adityabhardwaj3495 3 роки тому +3

      @@surelock3221 bro, they taught you this topic in the 11th grade? here we just learn continuity in the 11th grade.

    • @surelock3221
      @surelock3221 3 роки тому +1

      @@adityabhardwaj3495 It might have been grade 12, I just realized I can't remember exactly who my teachers were for those classes, or if it was the same person for both

    • @kirinvey2649
      @kirinvey2649 3 роки тому +1

      @@adityabhardwaj3495 bruh Im learning this for my 9th-grade pre calc final rn smh.

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    @andreferreira2693 Рік тому +9

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  • @peydee_364
    @peydee_364 2 роки тому +16

    you're the only reason why I even have a chance at passing my calc 2 midterm tomorrow

    • @Aj_chan0130
      @Aj_chan0130 2 роки тому

      bro same i have a test tomorrow this guy is fr the goat. Thanks Teach

  • @patrickmayer9218
    @patrickmayer9218 2 роки тому +7

    1. In the a/(1-r) formula, a is just a sub 1.
    2. The abs(r) < 1 is just a check to see if you can use the a/(1-r) formula.

  • @DaiMoscv
    @DaiMoscv 2 роки тому +7

    14:36 there is easier way, if SUM(n=m) then (ar^m)/1-r. So in our case our m = 1, a = 5, r = 8/25. If you follow the equation you'll get same answer as in the video 40/17 .

  • @kinslayer3609
    @kinslayer3609 5 років тому +33

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    @carolyndokes5350 2 роки тому +1

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    @konabos747 10 місяців тому +1

    Thank you for helping so many college students throughout the years. I am so grateful for this channel's existence and I owe my college degree to you.

  • @monishjain1113
    @monishjain1113 Рік тому

    A whole day of not understanding my Calculus professor and textbook, and this video taught me all of it within 15 mins! Many thanks!

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    @arnoldtaiwo5604 2 роки тому

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  • @Rawya-te4fs
    @Rawya-te4fs 6 місяців тому

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  • @xeli3046
    @xeli3046 4 роки тому +35

    To all further maths students: do you know the feeling when you've already studied a subject like this and then forgetting what you've learned years after the years???
    Yeah, that's how I feel rn :(

    • @justsam0511
      @justsam0511 3 роки тому +1

      But it's like riding a bike. We can get back on easier second time.

    • @drumman22
      @drumman22 3 роки тому +1

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    • @_Cfocus
      @_Cfocus 8 місяців тому

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  • @God-yd8zh
    @God-yd8zh 2 роки тому +1

    Thank you sir for teaching my lesson.

  • @aymanhijjawi9869
    @aymanhijjawi9869 3 роки тому +4

    I watched this and now I'm a mathematician by genetics !

  • @Benedict_Miriti
    @Benedict_Miriti 5 років тому +10

    Thank you so much.After watching the lecture video on finding the sum of infinite geometric series, i have been able to complete my assignment.You surely cannot go wrong with this lecturer.

  • @eliseerickson5994
    @eliseerickson5994 5 років тому +10

    I looked at my calc notes today for a test and nothing made sense after a month. I don't ever remember my teacher explaining it like this but I finally understand something!!

  • @A_B_1917
    @A_B_1917 4 роки тому +10

    Pro tip about the (2^3n)*(5^1-2n).
    When you get to the point where there is sigma of "5*(8/25)^n" you actually CAN use formulas. You can tranform it into "5*(8/25)*(8/25)^(n-1)", so that it fits formula with sigma starting from 1.

    • @sandilemposula3538
      @sandilemposula3538 4 роки тому

      How do you do that, please send me via e-mail.My e-mail is smposula300@gmail.com.Please m writing this Monday.

    • @Notthisagain28
      @Notthisagain28 2 роки тому +1

      This will NOT give you the same answer which is 40/17. This instead gives you 200/17. WRONG ANSWER

  • @damsellette
    @damsellette 3 роки тому +1

    akutami sensei makes me learn this lesson

  • @juulia287
    @juulia287 2 роки тому

    dude is literally my life saver. I have a math final on Tuesday on this lesson, this will rly help me

  • @mochii1908
    @mochii1908 3 роки тому +1

    i always go to this guy whenever there's a lesson I can't understand from my teacher..

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    @victorjohnson-c6t 8 місяців тому

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  • @-avalon-9440
    @-avalon-9440 4 роки тому +1

    This guy is way more useful then my teacher

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    @SuperG3FR 6 років тому +18

    Best guy ever

  • @phelhadsu4080
    @phelhadsu4080 3 роки тому

    your students must be so lucky to have you

  • @leumasgrountiez5647
    @leumasgrountiez5647 2 роки тому

    This helped me since i got confused at my teachers explanation

  • @Radon27
    @Radon27 7 місяців тому +1

    00:02 Finding the sum of an infinite geometric series using a formula
    02:20 Finding the sum of an infinite geometric series using common ratio
    04:41 Explaining calculation of the sum of an Infinite Geometric Series
    07:04 Finding the sum of an Infinite Geometric Series
    09:32 Sum of series with exponential terms
    12:17 Finding the first term and common ratio of an infinite geometric series
    14:45 Summarizing the method to find the sum of an Infinite Geometric Series
    17:23 Determining the sum of the infinite geometric series.

  • @yassine321
    @yassine321 4 роки тому +3

    Thanks a lot i really appreciate those lectures and also the lectures of thermodynamics

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    @niccoloripamonti6501 2 роки тому +2

    my worst fear is that one day I will have to learn something that you havent covered on the channel :(

  • @nelsonphiri7914
    @nelsonphiri7914 2 роки тому

    This guy is the best.

  • @Flower-cu5li
    @Flower-cu5li 4 роки тому +3

    Thank you! Very straightforward video.

  • @angusmothusi
    @angusmothusi Місяць тому +1

    for one of the problems how do you know the value of e??

  • @noelamassawe1602
    @noelamassawe1602 2 роки тому +1

    Your content are amaizing

  • @spandanshakya8031
    @spandanshakya8031 2 роки тому +1

    love you mate

  • @marielle6673
    @marielle6673 Рік тому

    This makes so much sense now! Thank you!

    • @justgab6851
      @justgab6851 Рік тому

      can we cancel out mixed numbers?

  • @tonyha8888
    @tonyha8888 4 роки тому +3

    We also have the same question. and if you factorised the numerator on the last question into 2^n(2^2+1)/5^n this simplified to 5(2/5)^n and we obtained a different answer which was 10/3

  • @vampsog7605
    @vampsog7605 7 місяців тому

    Thank you sir, you are a life saver.

  • @AnanomousRex
    @AnanomousRex 11 місяців тому

    your a legend bro, love you very much

  • @juanpabloberruochoa6367
    @juanpabloberruochoa6367 Місяць тому

    The Lord has provided us once again

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    @RediteeyobBijiga 8 місяців тому

    May God bless you i have no word for you

  • @aashsyed1277
    @aashsyed1277 3 роки тому

    3 m subscribers!!!!! I'm excited!!!

  • @user-sr1pp7sv9q
    @user-sr1pp7sv9q 2 роки тому

    You might’ve just saved me from failing my exam tomorrow. Fingers crossed.

  • @jossadesamito9552
    @jossadesamito9552 4 роки тому +2

    THANK YOU SO MUCH! ❤️

  • @VILOHIT
    @VILOHIT Рік тому

    your methods are good

  • @nishadr.7637
    @nishadr.7637 3 роки тому +1

    I understood everything in the first 3 minutes, this is a very helpful video

  • @carsonbarnes1834
    @carsonbarnes1834 3 роки тому +1

    god bless this man

  • @ST-od1br
    @ST-od1br 5 років тому +7

    Btw UA-cam keep adding adds telling students that they can get better education by leaving UA-cam education channels that can destroy your work .. just saying 😐

    • @kameronbriggs235
      @kameronbriggs235 5 років тому +4

      Yeah but anyone who follows these, knows they are great. I got like almost 170 videos of his down, and im going to finish this entire calculus playlist of 226.
      People are here for a reason.

  • @sumsolution1064
    @sumsolution1064 2 роки тому

    Speechless sir....

  • @JustBaileey
    @JustBaileey 2 роки тому

    Exactly what I was looking for. I can make the assumption that if r>1 the series must be diverging.

  • @issachernandez1828
    @issachernandez1828 6 років тому +1

    Better than my instructor and sloppy notes, Thanks!

  • @mahidertihtina4852
    @mahidertihtina4852 7 місяців тому

    Love this guy.

  • @georgesadler7830
    @georgesadler7830 3 роки тому +1

    Professor Organic Chemistry Tutor, thank you for explaining The Sum of an Infinite Geometric Series in Calculus Two. Geometric Series are very important in Advanced Mathematics/Engineering. Geometric Series is also used in Signal and Systems Theory and Digital Signal Processing. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.

  • @geektoys370
    @geektoys370 2 роки тому

    You are a legend

  • @bepositive3514
    @bepositive3514 4 роки тому +1

    Thank you very much for this great video🤩

  • @malxruxes6704
    @malxruxes6704 5 років тому

    The gift that keeps on giving

  • @milenamijuskovic2340
    @milenamijuskovic2340 6 років тому +10

    You are literally saving me, but can you please please do one where r is bigger than one? For example idk how to solve; sigma( 1 to infiity) of 1^n/(n^6) -_-' :(

    • @WittyComm3nter
      @WittyComm3nter 5 років тому +4

      I know you're progabaly not concerned with this answer anymore. But that's a p series not a geometric series. the P value (which is 6) is > 1 so it converges by p series test. According to the online calculator wolfram alpha it converges to 1.0173..... wolfram alpha used comparison test.

    • @fitnessabdul6811
      @fitnessabdul6811 4 роки тому

      @@WittyComm3nter Ok.

  • @RRatedT
    @RRatedT 4 роки тому

    Thank you so much, I finally understand what I'm suppose to do.

  • @hopeschroder8122
    @hopeschroder8122 3 роки тому

    thank you very much ,this helped out a lot

  • @noelamassawe1602
    @noelamassawe1602 2 роки тому +1

    Please can you do a video
    About expansion of e^x
    To find sum of geometric series using e^x

  • @robynslater95
    @robynslater95 8 місяців тому

    I like these series because you can see what it will converge to if it does

  • @arvindkannan867
    @arvindkannan867 5 років тому +6

    thank you so much. I do have a doubt though. in the last problem, why did you split the fraction as 4/5 + 2/5?? why couldn't we solve without splitting the fraction? like then , first term would then be 6/5 and common ratio would be 2/3 and the total sum then would be 18/5. can you please clarify?

    • @tonyha8888
      @tonyha8888 4 роки тому +1

      We also have the same question. and if you factorised the numerator on the last question into 2^n(2^2+1)/5^n this simplified to 5(2/5)^n and we obtained a different answer which was 10/3

    • @jimhalpert9803
      @jimhalpert9803 4 роки тому +1

      I tried without splitting and it wasn't forming a geometric series as the r differed in value when I tried a2/a1 and a3/a2

    • @morganblarue
      @morganblarue Рік тому

      @@jimhalpert9803 YES. This was my question. Thank you, Jim, for explaining!

  • @ryguy2368
    @ryguy2368 2 роки тому

    Absolute legend

  • @alexbutterboy9807
    @alexbutterboy9807 2 роки тому +1

    Why did you multiply by 2 at 1:48

  • @3515B1
    @3515B1 3 роки тому +1

    I will give you a shout out📢📢 when I graduate for sure 👨🏽‍🎓

  • @AlexRose-qd3or
    @AlexRose-qd3or Рік тому

    Thank you so much for all of the math tutorials you've made, they've helped so much.
    Do you think you can make your voice a little bit louder though? It gets hard to hear your explanations any time there's even a little bit of background noise.

  • @anipurasu
    @anipurasu Рік тому

    Thank you sooooooooo much ❤

  • @jimdolloso2331
    @jimdolloso2331 3 роки тому

    Your a genius 🤧

  • @sunduspp7123
    @sunduspp7123 4 роки тому +1

    sir your lectures are awesome
    but can you make it a bit louder [it is less audible]

  • @masonwong895
    @masonwong895 5 років тому

    This is a really good video!!!!!!!!!!!!!!!!

  • @muhammadahmadmuhammadahmad77

    Thanku so much sir

  • @awightviewuhs6103
    @awightviewuhs6103 3 роки тому

    this video has taught me more in 3 minutes then my entire summer school math lesson

  • @elijahcota2408
    @elijahcota2408 3 роки тому

    Thank you

  • @amnajamal4298
    @amnajamal4298 3 роки тому +1

    Can you please explain how you come to the exponential number at the end?

  • @iinnamorasii
    @iinnamorasii 2 роки тому +1

    so in the first example why did you multiply both 8 and 1-1/2 by 2

  • @effawannie2149
    @effawannie2149 2 роки тому

    thank you!!!

  • @adanvivero702
    @adanvivero702 5 років тому +1

    you are a hero

  • @spicy_tomato641
    @spicy_tomato641 4 роки тому +2

    Sir I have a question why did you multiply by 2 in 1:40?
    Edit: Now I know why. Im just gonna leave this comment here to remind people that some people are slower than others and thats okay.

    • @aki8683
      @aki8683 4 роки тому

      Wait what's the reason tho?

    • @spicy_tomato641
      @spicy_tomato641 4 роки тому

      @@aki8683
      because of the 1/2 the denominator is 2

    • @aki8683
      @aki8683 4 роки тому

      @@spicy_tomato641 Ohh okay thanksss

    • @queenosas7774
      @queenosas7774 8 місяців тому

      ​@@spicy_tomato641 does that automatically rule out the denominator??

    • @spicy_tomato641
      @spicy_tomato641 8 місяців тому

      Lets be realistic here. Its been 3 years. I already forgot. AHAHAHAHAHAHA​@@queenosas7774

  • @victorcastrellon4880
    @victorcastrellon4880 3 роки тому

    great video, than you

  • @zonborromeo6867
    @zonborromeo6867 Рік тому +1

    Please pray for me for my calculus exams tomorrow 😭

  • @yixuhoon6125
    @yixuhoon6125 8 місяців тому

    Hey can you make a playlist on linear algebra.. Space and base staff

  • @NancySam-vd5xh
    @NancySam-vd5xh 9 місяців тому

    Ur the best!

  • @zack_120
    @zack_120 3 роки тому +1

    15:30 - Didn't you say earlier in this video that the summand's power should be (n-1) if n starts from 1, and should be n if n starts from 0? Why the power = n here while n starts from 1? That is, the a₀ term is missing.

  • @manuelcardoso7595
    @manuelcardoso7595 2 роки тому +2

    I'm 13 years old (almost 14 though), I'm portuguese and his explanation is so good, that I understood it, even though it's in english.

  • @sukhkaur444
    @sukhkaur444 4 роки тому

    @ 3:55 (second # problem). 3*3*3 is 27. YOU put 9. Please check for the right ans. Let me know

    • @sukhkaur444
      @sukhkaur444 4 роки тому

      SO the answer should be 27.

    • @sukhkaur444
      @sukhkaur444 4 роки тому

      My bad I see you are multiplying not squaring. OMG sorry

  • @mike22bball82
    @mike22bball82 5 днів тому

    The GOAT

  • @EarlJovenSuyo
    @EarlJovenSuyo Рік тому

    I just watched this and my exam is within an hour.

  • @therohan1957
    @therohan1957 3 роки тому

    Well sir I might just actually pass this test

  • @queenosas7774
    @queenosas7774 8 місяців тому

    Thank you so much but d part not yet clear for me is when we multiple both side with the denominator does that automatically rule out the denominator itself??

  • @AlbertoRivas13
    @AlbertoRivas13 5 років тому

    thanks bro

  • @iskaiah9239
    @iskaiah9239 5 років тому

    Thankyou! Very understandable! 💖

  • @Kasfas
    @Kasfas 6 років тому

    I’ve been trying to get this for days now and only now understood it.
    I’m going to keep this one stored away for future reference.

  • @nifabcy
    @nifabcy 3 місяці тому +1

    I'm having mental breakdown while watching, why did you multiply it by two😭😭😭 on the first ex.

    • @Abby-in6tk
      @Abby-in6tk 2 місяці тому +1

      Hopefully you're doing OK but just in case, I believe he multiplied by 2 to make the 1-1/2 easier to visually work with by making all the numbers whole (i.e 1-1/2 -> 2-1). So instead of having a fraction in the denominator, he has all whole numbers. Technically it was easy to solve without doing so, but I think it looks cleaner that way when explaining