Alternating Series Test

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  • Опубліковано 29 бер 2018
  • This calculus 2 video tutorial provides a basic introduction into the alternating series test and how to use it to determine the convergence and divergence of a series.
    Integral Test For Divergence: • Calculus 2 - Integral ...
    Remainder Estimate - Integral Test:
    • Remainder Estimate For...
    P-Series:
    • P-series
    Direct Comparison Test:
    • Direct Comparison Test...
    Limit Comparison Test:
    • Limit Comparison Test
    _________________________________
    Alternating Series Test:
    • Alternating Series Test
    Alternate Series Estimation Theorem:
    • Alternate Series Estim...
    Absolute & Conditional Convergence:
    • Absolute Convergence, ...
    The Ratio Test:
    • Ratio Test
    The Root Test:
    • Root Test
    __________________________________
    Series Tests - Practice Problems:
    • Calculus 2 - Geometric...
    Taylor & Maclaurin Polynomials:
    • Taylor Polynomials & M...
    Taylor's Remainder Theorem:
    • Taylor's Remainder The...
    Power Series - Interval Convergence:
    • Power Series - Finding...
    Power Series - Derivatives & Integrals:
    • Power Series - Differe...
    ___________________________________
    Calculus Final Exam and Video Playlists:
    www.video-tutor.net/
    Full-Length Videos and Worksheets:
    / collections

КОМЕНТАРІ • 204

  • @TheOrganicChemistryTutor
    @TheOrganicChemistryTutor  Рік тому +13

    Next Video: ua-cam.com/video/FkUrAgBzAZo/v-deo.html
    Final Exams and Video Playlists: www.video-tutor.net/

  • @itllbeokay7112
    @itllbeokay7112 5 років тому +850

    You've got this. Stop reading comments and go study to ace that test.
    Or pass that test whatever your goal is

    • @SyrinSlava
      @SyrinSlava 4 роки тому +35

      At this rate, my only chance is a C lmao.

    • @Yo-pn9qp
      @Yo-pn9qp 4 роки тому +1

      Thanks boo

    • @zozozoz2460
      @zozozoz2460 4 роки тому

      اي صدك ما تنفهم

    • @zozozoz2460
      @zozozoz2460 4 роки тому +2

      😂😂😂😂😭😭

    • @ignantxxxninja
      @ignantxxxninja 3 роки тому +1

      @it'll be okay & @Sleeve Them All that was very motivating

  • @hsc4648
    @hsc4648 4 роки тому +601

    Seems so easy when you look at his video but by the time I get to my university text book lol the difficulty of the problems are totally on another level.

    • @sofir9400
      @sofir9400 4 роки тому +32

      right its completely diff lmao

    • @kaylao.7688
      @kaylao.7688 4 роки тому +5

      @@sofir9400 felt that...

    • @ferry6700
      @ferry6700 4 роки тому +22

      Univ text book is shit :'(

    • @ryzurrin
      @ryzurrin 3 роки тому +3

      exactly the case :(

    • @AbdoAhmed-qw3le
      @AbdoAhmed-qw3le 3 роки тому +6

      @@kaylao.7688 never knew shit could be so expensive 😭😭😭

  • @meerasrinivasan9481
    @meerasrinivasan9481 3 роки тому +201

    You seriously are the greatest of all time. I had Calc 1 last semester and watched your videos instead of lecture because you explain things so clearly and do the algebra really well. Aced that class thanks to you! Now acing calculus 2 with your videos, once again. Wishing you the most success and happiness!! You have such a big impact on math students - esp ones like me who genuinely never thought I'd even get through calc 1 let alone 2!

  • @luciogaribay4321
    @luciogaribay4321 5 років тому +107

    I’m currently taking calculus 2 in the summer and it is brutal but these videos keep me going. They make everything more simple to learn.

    • @chrismason1530
      @chrismason1530 2 роки тому

      Same

    • @leif1075
      @leif1075 Рік тому

      Why is it brutal?

    • @potatotuna7988
      @potatotuna7988 Рік тому

      @@leif1075 calculus can be pretty hardddd

    • @calebfoxschool
      @calebfoxschool Рік тому +4

      @@leif1075 As someone who took Calc 1 over the summer, it's just a lot to take in at once. With jumping all around from integral techniques, physics problems, parametric/polar equations, and now series/sequences, I can imagine it would be hard to grasp all the concepts in a short amount of time.

    • @ash-lo2dc
      @ash-lo2dc Рік тому

      @@leif1075 summer semesters are kinda short iirc

  • @ahmedjamshaid7727
    @ahmedjamshaid7727 3 роки тому +90

    Just amazing, and I couldn't understand my professor's 4 hours of lectures

  • @maameabena514
    @maameabena514 3 роки тому +22

    You're the best thing that ever happened to my college career

  • @its1haruka1dayo
    @its1haruka1dayo 3 роки тому +6

    I was about to cry because I didn't understand a word until I watched this video
    THANK YOU THREE YEARS LATER!!

  • @zhouj8634
    @zhouj8634 5 років тому +33

    I love all of your videos. They help me a lot. I just want to point out one thing in this video: at the 6 minutes mark, you said :”The test is failed, so the series diverges.” Alternating series test just can prove convergence, can not prove divergent. So the conclusion should be inconclusive. If the test failed, we should use other test to define convergence or divergent.

    • @armandoolmos1816
      @armandoolmos1816 4 роки тому +1

      Zhou J This should be pinned as top comment so anyone learning the A.S.T would know that it only proves convergence.

    • @griffinewine615
      @griffinewine615 4 роки тому

      This is correct

    • @reemabedair9223
      @reemabedair9223 2 роки тому +2

      I know I'm late, but he said in the beginning of the video that if the first test fails, you can consider that as automatically diverging

    • @ARTDEVGRU247
      @ARTDEVGRU247 Рік тому

      Yea i picked up on that

    • @beasttech4330
      @beasttech4330 9 днів тому +1

      He did divergence test

  • @nurayim6295
    @nurayim6295 Рік тому +4

    Words can't expess how I'm grateful. Our teacher just reads off the presentations during lectures and I don't understand anything, but thanks to you I'm easily passing all of the quizes, homeworks and mid/end term exams. Got only the final exam left to pass, thanks a lot for saving my degree😭❤

  • @shijialiu8678
    @shijialiu8678 3 роки тому

    Thank you so much! This is extremely helpful and your demonstration is so clear!

  • @ammaralsawai7724
    @ammaralsawai7724 5 років тому +97

    You should be the one I pay

    • @itllbeokay7112
      @itllbeokay7112 5 років тому +11

      You can do that by watching his ads:)

  • @joshuaabbott7134
    @joshuaabbott7134 5 років тому +37

    Your videos make so much more sense than my professor! Thank you!!!

  • @chrisp2639
    @chrisp2639 Рік тому +8

    Between your videos and Paul's Notes for additional practice problems, I have an A+ in calculus 2. Thank you!

  • @hibanazar9039
    @hibanazar9039 2 роки тому +1

    The methods are way more easier.
    Thank you so much.

  • @abdulrahmanyasser3897
    @abdulrahmanyasser3897 6 років тому +1

    ...thanks dude u r awesome ...i really understood math on ur hands

  • @Just_A_Transperson
    @Just_A_Transperson 7 місяців тому

    Thank you so much. You got me a 5 on AP calc, and you care getting me through calc 2 in collage.

  • @liquidice1677
    @liquidice1677 7 днів тому

    GREAT VIDEO!!!! Also a note is that this video is about conditional convergence. Alternate series can converge in a different manner known as absolute convergence, and the test for that is if the absolute value of an alternating series (an) converges, then the series converges absolutely and you dont need to check for conditional convergence.

  • @genogurirab8061
    @genogurirab8061 2 роки тому +2

    You are talented really the absolute king

  • @frankimhof8124
    @frankimhof8124 5 років тому

    man I love your videos. They're so clear and easy to follow. Thanks a lot!

  • @adabujiki
    @adabujiki 4 роки тому +2

    Lol this guy knows my deep frustrations with this concept-- I COULD NEVER FIGURE OUT WHAT A-sub-n was in the function... turns out it was the quotient 1/n... when one sees a bunch of "n" variables everywhere it is hard to tell how to solve it. THANKS BRO... be nice to show ur face one day so we can profile u and make assumptions of u

  • @rap33r100
    @rap33r100 5 років тому +60

    It would be more accurately described as it needs to fail the divergence test. As passing the test implies its divergent. Other than that excellent video

    • @eric693
      @eric693 5 років тому +5

      One of my classmates was confused over the meaning of passing or failing the test. Although it is kind of odd to say "failing" when it satisfies the conditions, but in this context, it would make sense to say failing the Divergence Test. It could be put in a way like the following: A checkpoint on the road to pick off a specific car. If a car doesn't satisfy the conditions, then it moves on -- passing the checkpoint. Whereas if a car meets the condition, it gets pulled off and fails to pass the checkpoint. I tried explaining it like that to her, but she doesn't seem to get it still. . .I mean both passing and failing makes sense in their own way.

    • @niche5006
      @niche5006 5 років тому +2

      @@eric693 I think of it like this: when a series passes a test then there is no need for another test because you have found the answer. Likewise, when you fail a test, you need to try another test to find convergence or divergence.

    • @mreleven7826
      @mreleven7826 5 років тому +3

      JMac he is correct . If u pass a drug test . What does that mean?

    • @angebomb
      @angebomb 4 роки тому +1

      YES! It took me an hour to realize that he was implying two different things lol

    • @lancematteson2416
      @lancematteson2416 3 роки тому

      That tripped me up for a bit! I had to go back and double check my notes; I thought I might have wrote the Divergence Test incorrectly! Once I realized he more meant that "this meets the first condition" I was able to get back on track.

  • @abidashaheen819
    @abidashaheen819 3 роки тому +1

    Great lecture 👍🏻👍🏻👍🏻👍🏻

  • @rajendramisir3530
    @rajendramisir3530 5 років тому +34

    Interesting: Harmonic series diverges by p-series test while alternating harmonic series converges by alternating series test.

    • @nicholasmaloof8378
      @nicholasmaloof8378 4 роки тому +3

      This tripped me up a bit

    • @Zephyr-tg9hu
      @Zephyr-tg9hu 4 роки тому +13

      This has always made little intuitive sense to me.
      Reminds me of some wise words once spoken by Von Neumann: "Young man, in mathematics you don't understand things. You just get used to them."

    • @chrischika7026
      @chrischika7026 3 роки тому

      bAy-Zesd

    • @kylejohnson1248
      @kylejohnson1248 2 роки тому +1

      Because it’s conditionally convergent, the convergence is caused by the negative.

    • @xEqualsRandom
      @xEqualsRandom Рік тому +1

      ​@@kylejohnson1248 I thought this video was a bit confusing because it doesn't mention convergence vs conditional convergence

  • @MrMarkgyuro
    @MrMarkgyuro 4 роки тому +1

    best video to understand this topic

  • @FaisalAl-Edaily
    @FaisalAl-Edaily 2 місяці тому

    I think you deserve way more than 7.88M Subs, Like seriously you explain so good I understand most of the stuff you explain (Not everything since i'm a 9 year old)

  • @onur7192
    @onur7192 5 років тому +1

    thx you so much my teacher it gonna be good for midterm1 :D

  • @mr.prince8701
    @mr.prince8701 6 років тому +2

    Great video as always.

  • @rotemlv
    @rotemlv 3 роки тому +6

    10:21
    n has to go from 2 here as the denominator is undefined at n = 1.

  • @candicechita9789
    @candicechita9789 Рік тому +1

    You never disappoint dude🥹

  • @yuxichi4245
    @yuxichi4245 4 роки тому

    IT IS REALLY HELPFUL!

  • @marmedrano4365
    @marmedrano4365 3 роки тому

    I love this man so much.

  • @NabharajShrestha
    @NabharajShrestha 5 років тому

    You are aweosome...
    Thank you soo much...

  • @theplasmatron3306
    @theplasmatron3306 8 місяців тому

    This awesome, I appreciate it. Thank you!

  • @sofiaizaguirre5779
    @sofiaizaguirre5779 6 років тому +1

    thank you so much

  • @jameson409
    @jameson409 4 роки тому +26

    who else is watching this in preparation for the AP calculus exam

  • @_towards_destination
    @_towards_destination 2 роки тому

    You are a pro man ♥️♥️ God bless you

  • @fahadsaleem5727
    @fahadsaleem5727 5 років тому

    bundle of thanks

  • @madhurakulkarni1880
    @madhurakulkarni1880 5 років тому

    Thank you so much sir ......

  • @frankvalen2147
    @frankvalen2147 3 роки тому +1

    why cant I just plug number like 1 in that question that has ln(n+1)/n+1

  • @ahankurdi1745
    @ahankurdi1745 3 роки тому +2

    You do better than all of my professors. You desire golden rewords. ❤️

  • @kafianan6586
    @kafianan6586 5 років тому

    {(1-lnx)/x^2}... How this function is increasing in the interval [1,e) ?
    Moreover, we get the max value of function when limit of [x] tends to 0... If I am wrong please make me correct.. Thank you

  • @nothingtoxicated5937
    @nothingtoxicated5937 4 роки тому +5

    You deserve more subscriber than Khan academy

  • @shyamyadla3515
    @shyamyadla3515 5 років тому

    Great job

  • @alifaziz3539
    @alifaziz3539 2 роки тому

    you are great ....😊 thank u so much

  • @cold_scene
    @cold_scene Рік тому

    you are amazing dude

  • @scoot115
    @scoot115 3 роки тому +6

    Organic Chemistry Tutor > Every college professor

  • @dilkinirasha9612
    @dilkinirasha9612 2 роки тому +1

    You can teach all the semesters within one semester.😍

  • @mathgmathg923
    @mathgmathg923 6 років тому +6

    You are AWESOME!!!!!

  • @colinjaros1710
    @colinjaros1710 3 роки тому

    Thank you !

  • @frka3176
    @frka3176 3 роки тому

    Can you really use L'Hôpitals rule at 5:40? I've always learned that functions need to be continuous for the derivative to exist, and normally I don't think you would say that a function defined on non compact set of ellements is continuous?

  • @SilentJnation
    @SilentJnation 2 місяці тому

    God bless you. Calc 2 final is tomorrow morning.

  • @uchennaobi5985
    @uchennaobi5985 5 років тому +2

    You are GOD like at teaching

  • @aaronfister2129
    @aaronfister2129 3 роки тому

    this mans doesn't miss

  • @bernadettelola638
    @bernadettelola638 3 роки тому

    Thank you

  • @memevideos7461
    @memevideos7461 Рік тому +1

    so you don't test if lim n-> infinity (whole expression using alternator) = 0 before using this alternating series test?

  • @georgesadler7830
    @georgesadler7830 2 роки тому +1

    Professor Organic Chemistry Tutor, thank you for an excellent video/lecture on the Alternating Series Test in Calculus Two. The Alternating Series Test is not a difficult test to understand, however checking for convergence can be problematic. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.

  • @tsholocarly4786
    @tsholocarly4786 Рік тому

    Such a genius😩

  • @farwamalik3028
    @farwamalik3028 2 роки тому

    Amazing 👌

  • @lootingpig9713
    @lootingpig9713 5 років тому +1

    gud stuff broski

  • @nikkim8098
    @nikkim8098 6 років тому +1

    thank you THANK YOU THANK YOUUUUUUUUU

    • @adios04
      @adios04 3 роки тому

      your very welcome!

  • @pranav-the-vagabond
    @pranav-the-vagabond 4 роки тому +1

    is it ok to differentiate numerator and denominator saperately?
    If yes, what do we get on differentiating them separately ?

    • @dev217
      @dev217 4 роки тому +2

      Differentiating the numerator and denominator separately is for L'Hopital's rule. When you get a limit in form inf/inf you can use L'Hopital rule to get a new function to work with.

  • @harshitbhandi5118
    @harshitbhandi5118 3 роки тому +1

    LIFE SAVERRRRR!!!!

  • @twinbruisesonmyshins
    @twinbruisesonmyshins 7 місяців тому

    this video actually saved my fucking life, i take cal2 and sequences/series are the last chapter before exams and they absolutely decimate me. i worked for eight hours on an assignment thats majority series and barely made any progress

  • @RcReventon
    @RcReventon 5 років тому

    for the ln(n)/n finding if the function decreases, why do we say that one of the critical points is 0 when setting the denominator equal to 0 will cause an indeterminate form?

    • @richie1603
      @richie1603 5 років тому

      I think because its indeterminate , you then move on to the next one

  • @A1T6J
    @A1T6J Рік тому

    Thanks Bro

  • @dhyeyranpara2351
    @dhyeyranpara2351 Рік тому

    not gonna lie, you should start your own virtual university. you just too good.

  • @subodh3797
    @subodh3797 Рік тому

    thanks bro

  • @ZkdlinXO
    @ZkdlinXO 6 місяців тому

    12:38 why we didn't use p series for 1/n which is divergent?

  • @soner8780
    @soner8780 5 років тому

    thanks

  • @rajendramisir3530
    @rajendramisir3530 5 років тому

    Must watch video for a variety of examples on each technique, topic or concept. I particularly like the cos(2pi) effect of creating an alternating series. I suppose sin(2pi) will have a similar effect.

  • @jaytao8124
    @jaytao8124 5 років тому

    In the last problem, I tried doing divergence test and applied L'Hopital's Rule for cos(npi)/n... I then got DNE as my answer??? Wouldnt it diverge instead?

    • @sarahkamal2585
      @sarahkamal2585 5 років тому +1

      I think it's because you are supposed to get the limit of An only which is (1/n). the cos(pi*n) is like (-1)^n. You can only apply the divergence test for positive series, therefore you wont get the right answer if u take the limit including the cos(pi*n). that's why we use this alternating test

  • @batuhank.758
    @batuhank.758 3 роки тому

    why didn't you use absolute convergence after conditionally convergence?

  • @ahankurdi1745
    @ahankurdi1745 3 роки тому

    Loved itt ❤️

  • @0Saqia0
    @0Saqia0 3 роки тому

    thank you x

    • @adios04
      @adios04 3 роки тому

      no problem

  • @sabilakensawitri3103
    @sabilakensawitri3103 4 роки тому

    and how to know the sum of series if its converge?

  • @Eric-oe6vd
    @Eric-oe6vd 4 роки тому +1

    Thanks, better than my prof x100

  • @energy9442
    @energy9442 2 роки тому

    thank u

  • @LL-kn1de
    @LL-kn1de 6 років тому

    Thank you!!!!!!!!!!!!!

    • @adios04
      @adios04 3 роки тому

      your welcome

  • @mpilow9463
    @mpilow9463 4 роки тому

    very useful video, Now I know Im alternating

  • @eduardogomez3653
    @eduardogomez3653 3 роки тому

    Did the series actually decrease in the first example because I thought n=1 equals -1 not 1 like he put

  • @alaazingi5784
    @alaazingi5784 2 роки тому +2

    i owe this guy my universitie's tuition

  • @bychyke9581
    @bychyke9581 5 років тому

    The question second to last: (ln/n) is divergent by the direct comparison test.

    • @shravipujari8672
      @shravipujari8672 3 роки тому

      No actually the test fails if we use direct comparison method as it is said that if summation an and summation bn are series of positive terms it should satisfy the condition that is
      1) summation bn is convergent then only summation an is convergent.
      2) if summation an is divergent then summation bn is divergent.... Nd in ln(n) / n.... 1/n diverges by the p series test but it is not following the giving condition which is said to be satisfied.

  • @wolfie6175
    @wolfie6175 3 роки тому +1

    we had assumed that an>0 but in the second example the denominator is negative for the first term which makes the fraction negative :/

  • @Adam-de8yi
    @Adam-de8yi Рік тому

    4 minutes it took me to understand a concept that my lecturer spent 2 hours discussing.

  • @lewiimetube4369
    @lewiimetube4369 2 роки тому +1

    Can the 1st condition be met and the 2nd one fail? Are there situations like those?

    • @JesusMartinez-zu3xl
      @JesusMartinez-zu3xl 2 роки тому +1

      both conditions need to be met in order for this series to be convergent. I know im late. lmfao.

  • @suturesgh4342
    @suturesgh4342 Рік тому

    Please what if its raised to the power n-1

  • @ultra3963
    @ultra3963 4 роки тому +2

    What if the limit is equal to 0, but it isn’t decreasing? Would it be convergent or dirvergent?

    • @reengaesh7545
      @reengaesh7545 4 роки тому

      Ultra Then I Think it will be divergent Bcz it can’t be convergent since both conditions are not fulfilled

    • @PrecisionCSGO
      @PrecisionCSGO 4 роки тому +1

      same, i was wondering this too!

    • @ARTDEVGRU247
      @ARTDEVGRU247 Рік тому

      Divergent, because for convergence, it must meet both conditions.

  • @LA-cm9uo
    @LA-cm9uo 4 місяці тому

    Thanks, in my university this topic goes under Calculus 1 still

  • @mohammedalnasri6574
    @mohammedalnasri6574 5 років тому

    legend

  • @richardfrederick1885
    @richardfrederick1885 3 місяці тому

    If you apply the AST with when An=1/n, then An goes to zero and it passes that part of the test. However, we know that 1/n is the harmonic series which is known to be divergent. There seems to be a contradiction here. How can it both approach zero and be divergent? Does it truly pass the test or not?

    • @pag651
      @pag651 2 місяці тому

      By the AST the alternating harmonic series (-1)^n (1/n) converges as the limit of the sequence, 1/n as n approaches infinity is zero, fulfilling the first criteria. The second criteria states that each iteration of the sequence must be smaller than the predecessor, which is also true for 1/n for the AST. Since those two criteria are fulfilled, it must mean that the alternating harmonic series (-1)^n (1/n) converges.
      However, the harmonic series in itself is divergent. It is true that the harmonic series 1/n approaches zero, and by the nth-term test, it doesn't fulfill the criteria for divergence. However, just because 1/n approaches zero does not mean it is automatically convergent, you must utilize other tests in order to see if the series is divergent or convergent. Imagine the nth-term as being the most general and broad filter that removes any series in which its sequence never approaches zero. For the case of harmonic series, if you take the integral of 1/n from 1 to b, in which b represents infinity, 1/n becomes ln(n). By the second FTC, the integral is represented by F(b) - F(1), in which F represents the antiderivative, ln(n). If we plug in infinity for n, realize that ln(∞) - ln(1) goes on to infinity, thus making the harmonic series 1/n divergent as it never converges to a definite value.

  • @highermaths
    @highermaths 2 роки тому

    helpful

  • @Dylan-ye7jb
    @Dylan-ye7jb 3 місяці тому

    cant believe im watching this video for a differential equations exam I took calc 2 an entire year ago i hate school so damn much

  • @user-vo2zv8nl7c
    @user-vo2zv8nl7c Рік тому

    Good

  • @jokerjoker8638
    @jokerjoker8638 4 роки тому

    Please anyone can help me find the nature of this series : Summation ( 1/ [ n + ((-1)^n)sqrt(n) ] )

  • @leoking2716
    @leoking2716 4 роки тому +1

    MY MY MY ==LEGEND

  • @faizamia9341
    @faizamia9341 2 місяці тому

    i love u thanks!

  • @kosuribalaji317
    @kosuribalaji317 3 роки тому +2

    I need complete real analysis short cuts

  • @MrPotaatooo
    @MrPotaatooo 4 роки тому

    for the last example: what if it was sin(n.pi) instead of cos(n.pi)

    • @askngunduz1776
      @askngunduz1776 2 роки тому

      it would just be 0 then.
      sin(pi)=0 , sin(2pi)=0 ...
      well i guess im too late to answer this but still :D

  • @donalddd8095
    @donalddd8095 5 років тому

    isnt the alternating series test cant show the series diverge?