Sequences | Convergence and Divergence

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  • เผยแพร่เมื่อ 28 ก.ย. 2024
  • We show convergence or divergence of some sequences.
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ความคิดเห็น • 92

  • @KOMATH
    @KOMATH  4 ปีที่แล้ว +18

    Typo in solution of 1: the difference in the numerator must be addition

    • @muhsinm4257
      @muhsinm4257 3 ปีที่แล้ว +1

      Sir, in 2nd question you take the divergent test , which says that if the limit n--》infinite (An) is not= 0 then it diverges.. but if the value is 0 then there is no conclusion that its converges or not ... so we need other testing method for it ..i was waiting for it. But sir just said which is converges.. how ?

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว +2

      @@muhsinm4257 The Divergence Test is only for series and not sequences. Don't be confused with convergence of sequences and series. The sequence a_n=1/n is convergent because its limit as n goes to infinity exists--it is 0; however, the series, sum of 1/n from n=1 to infinity, is divergent. That is well known as harmonic series.

  • @99BeastMaker
    @99BeastMaker 3 ปีที่แล้ว +28

    I like how everything is just so conventional...there are no difficult problems or easy problems...we just have problems...so calming

  • @adithya5435
    @adithya5435 3 ปีที่แล้ว +7

    Crisp and Concise, helped a lot :)

  • @steff.y2001
    @steff.y2001 3 ปีที่แล้ว +2

    Woww!! Helped me understand the limits of sequence better.

  • @alirezaansari7208
    @alirezaansari7208 10 หลายเดือนก่อน

    Thanks for explanation, do you have video for proving that as well?

  • @MahdiMahdi-ob9yo
    @MahdiMahdi-ob9yo ปีที่แล้ว

    Quand utilise-t-on la règle de L'Hubetal ?? Est à 0/0 et aussi à &/&

  • @raviramkiranbharadwaj6676
    @raviramkiranbharadwaj6676 3 ปีที่แล้ว +1

    Good work sir it really very easy understand thank u for this video

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว

      Glad it helped

  • @PratimMukherjee
    @PratimMukherjee 4 ปีที่แล้ว

    When I am asked to test whether the series is convergent or divergent
    I proceed as an+1 - an and i check if it's less than 0 and finally put limit n-♾️ in an

  • @halavathudhairyavalli3088
    @halavathudhairyavalli3088 3 ปีที่แล้ว

    Sir in 1st problem, if we take n^4 common answer is 1. Then it will be convergent sir. Please clarify my doubt sir.

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว

      Could you clarify your question? If you meant that if the leading term in the denominator is n^4 then the answer is 1, then you are correct.

  • @khairinmasturahbintiabdulh2127
    @khairinmasturahbintiabdulh2127 ปีที่แล้ว

    hi sir, may i know on question 3, why did you multiply the numerator and denominator with 1/squareroot n3?

    • @KOMATH
      @KOMATH  ปีที่แล้ว

      Hello. Squareroot of n^3 is like the dominant term in the denominator. Similar strategy with finding limits at infinity of rational functions where we divide all the terms in the numerator and denominator by the highest power of x in the denominator.

  • @jeroomonica9312
    @jeroomonica9312 ปีที่แล้ว

    Perfect 👍.. it's so understandable

  • @LenaAbanda
    @LenaAbanda 8 หลายเดือนก่อน +1

    Please for the first exercise why did you change the sign of 3 in the numerator?from +3 to -3

  • @michaelanit697
    @michaelanit697 4 ปีที่แล้ว

    ((n+2)^25/2^n+3)(2n/(n+5)^25) Please help me answer this sir..

    • @KOMATH
      @KOMATH  4 ปีที่แล้ว +1

      You can show that (n+2)^25/(n+5)^25 goes to 1 and 2n/(2^n+3) goes to 0 so that sequence approach 0.

  • @yffjggeyit2771
    @yffjggeyit2771 7 หลายเดือนก่อน

    بالنسبه للمثال الأول لازم نقسم على أكبر اس n4

  • @AFCOE
    @AFCOE ปีที่แล้ว +1

    ❤❤❤❤. But you didn't time the exercises😭

    • @KOMATH
      @KOMATH  ปีที่แล้ว

      😂

  • @mcqueenyt8883
    @mcqueenyt8883 3 ปีที่แล้ว

    Very helpful thank youuuu💕

  • @sandeepdappi6729
    @sandeepdappi6729 3 ปีที่แล้ว +3

    Very helpful sir,make more videos for bsc 5th semester

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว

      Glad to help. More videos coming soon🙂

  • @kavyasrivastava8694
    @kavyasrivastava8694 3 หลายเดือนก่อน

    what is the use and aplication of these pls someone tel me >.< ahh!!!!!!!!!!!

  • @mankoodhiman3861
    @mankoodhiman3861 3 ปีที่แล้ว +2

    It's really helpful video... Thanku so much sir..

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว

      Glad it helps!

  • @stevenewton3864
    @stevenewton3864 2 ปีที่แล้ว +1

    Perfect 👍🏼👍🏼it's resourceful

  • @andrestejeiro5538
    @andrestejeiro5538 3 ปีที่แล้ว +1

    great selection of examples. thank you

  • @yebook..
    @yebook.. ปีที่แล้ว +1

    Very helpful.

  • @LenaAbanda
    @LenaAbanda 8 หลายเดือนก่อน

    Please for the first exercise why did you change the sign of 3 in the numerator?from +3 to -3

    • @KOMATH
      @KOMATH  7 หลายเดือนก่อน

      Sorry that is a mistake as written in the pinned comment.😊

  • @morobamber3090
    @morobamber3090 3 ปีที่แล้ว +1

    God send

  • @amanrajput826
    @amanrajput826 3 ปีที่แล้ว +1

    Thanks Sir

  • @HabibaMusonda
    @HabibaMusonda หลายเดือนก่อน

    I am confused (question 3) how are we having √n after dividing n^2 in √n^3

  • @naruto_1113
    @naruto_1113 ปีที่แล้ว

    Hello sir,
    (1+1/n)^-5 is convergent but how to find its boundness
    Please sir explain this my exams are coming

  • @ThomasMunembome
    @ThomasMunembome 3 หลายเดือนก่อน

    Why n=0

  • @nguyendk410
    @nguyendk410 2 ปีที่แล้ว +1

    Dear Professor K.O.MATH,
    In question 7, how could we know that we divide both denominator and numerator for 3^n? Thank you very much.

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว +1

      Because it is the dominant term in the denominator, similar to the technique when finding limits at infinity of rational functions.

  • @nahiakhan2135
    @nahiakhan2135 ปีที่แล้ว

    THANKYOU SO MUCH SIR..
    RESPECT FROM PAKISTAN

  • @athiralalup7464
    @athiralalup7464 3 ปีที่แล้ว

    Very helpful video,thankuu sir🙏

  • @mdshaadalam2917
    @mdshaadalam2917 3 ปีที่แล้ว

    How can you say if limit of nth term is zero when n tends to infinity...you are wrong here sir... Because we can not tell the convergence or divergence of it for sure...we need further test...sir plzz cheak it.. For example if An=1/n in this case your method fails..

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว +5

      Don't be confused with convergence of sequences and series. The sequence a_n=1/n is convergent because its limit as n goes to infinity exists--it is 0; however, the series, sum of 1/n from n=1 to infinity, is divergent. That is well known as harmonic series.

  • @GentilleKubwayezu
    @GentilleKubwayezu ปีที่แล้ว

    I wanna to know about eigenvalues

  • @nguyendk410
    @nguyendk410 2 ปีที่แล้ว

    Dear Professor K.O.MATH,
    How could I find the limit of this sequence an = 3^n / 4^n
    Thank you so much.

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว +1

      This can be written as (3/4)^n and because |3/4|

  • @kunalgamerr007
    @kunalgamerr007 ปีที่แล้ว

    2nd question m 1+1/x kaise aya koi btaega

  • @rinentrishamaem.6753
    @rinentrishamaem.6753 3 ปีที่แล้ว

    Please help me in this question sir. Un=2n/5n-3. Determine if it is convergent or divergent.thankyou

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว +1

      Divide the numerator and denominator by n then you can easily determine the limit. And from there you can determine whether it is convergent or divergent.

  • @boamahjuniorsampson8564
    @boamahjuniorsampson8564 2 ปีที่แล้ว

    Impressive taught 👏 👌

  • @thebluebeyond2329
    @thebluebeyond2329 3 ปีที่แล้ว

    My new favorite math channel

  • @hakunaJ.A.
    @hakunaJ.A. ปีที่แล้ว

    Hello po pwese magtanong a number 3 po infinity divided by 1 infinity po ba answer? Hindi po 0?

    • @KOMATH
      @KOMATH  ปีที่แล้ว

      Hello Jessa. Tama na kapag ang numerator ay papuntang infinity at ang denominator ay papuntang 1, yung fraction ay papunpang infinity/1 o infinity. Pero kapag pagpilitin ang numerator at denominator, magiging 1/infinity at yang ang papuntang 0.😊

  • @akashhuyaar
    @akashhuyaar 3 ปีที่แล้ว

    Can you tell me convergence for An=3^n/n^2

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว +1

      You can tell the convergence by applying ratio test.

  • @lalisach0115
    @lalisach0115 2 ปีที่แล้ว

    thankyuo kan bira dabali ammas

  • @mathdude9287
    @mathdude9287 2 ปีที่แล้ว

    How do you say an is convergent surely when an = 0 because it is necessary but not sufficient....please correct it will confuse many student..

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว +3

      Don't be confused with convergence of sequences and series. The sequence a_n=1/n is convergent because its limit as n goes to infinity exists--it is 0; however, the series, sum of 1/n from n=1 to infinity, is divergent. That is well known as harmonic series.

    • @mathdude9287
      @mathdude9287 2 ปีที่แล้ว +2

      @@KOMATH Thanks for explaination.

  • @AnshuSharma-rm2bf
    @AnshuSharma-rm2bf 3 ปีที่แล้ว

    In 8 que. It should be divergent. Plz someone explain..

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว

      It is convergent as the limit exists. May I know why you think it is divergent?

  • @salivaryemily6766
    @salivaryemily6766 2 ปีที่แล้ว

    in question 5, the limit is not equal to zero. shouldnt it be divergent?

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว

      Don't be confused with convergence of sequences and series. A sequence is convergent if the limit exists, that is, the limit is a real number. Foe example, the sequence a_n=1/n is convergent because its limit as n goes to infinity exists--it is 0; however, the series, sum of 1/n from n=1 to infinity, is divergent. That is well known as harmonic series.

  • @benjamincheung4999
    @benjamincheung4999 2 ปีที่แล้ว

    Solution for number 7 is wrong, right? Shouldn't it be 0?

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว

      Hello Benjamin! Which part is wrong? It seems that there is nothing wrong in the solution.

  • @razdan.r3618
    @razdan.r3618 3 ปีที่แล้ว

    ありがと先生

  • @nguyendk410
    @nguyendk410 2 ปีที่แล้ว

    Dear Professor,
    How could I find the (n-3)! please?

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว

      (n-3)!=(n-3)(n-4)...(2)(1)

  • @girijasankarmandal1138
    @girijasankarmandal1138 ปีที่แล้ว

    Sir kindly solve this problem \{(2n ^ 2 + 1)/(2n ^ 2 - 1)\}The sequence
    converges to

    • @KOMATH
      @KOMATH  ปีที่แล้ว +1

      This is similar to problem 1. Divide all the terms in your numerator and denominator by n^2, simplify the little fractions, and from there you can easily determine the number to which it converges.

    • @girijasankarmandal1138
      @girijasankarmandal1138 ปีที่แล้ว

      @@KOMATH thank you very much sir

  • @danielbrown1933
    @danielbrown1933 ปีที่แล้ว

    19:00

  • @sarafatima3946
    @sarafatima3946 3 ปีที่แล้ว

    👍🏿

  • @ranjanasri6094
    @ranjanasri6094 2 ปีที่แล้ว

    Helps me a lot. Thank u so much sir

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว

      Glad it helped!

  • @mohammedmatinjasiibaway4329
    @mohammedmatinjasiibaway4329 2 ปีที่แล้ว

    God bless you sir🙏

    • @KOMATH
      @KOMATH  2 ปีที่แล้ว

      Thank you and same to you sir!

  • @michellz-y4p
    @michellz-y4p 3 ปีที่แล้ว

    What if n -> 25

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว

      At what time in the video?

  • @nidhigupta3203
    @nidhigupta3203 3 ปีที่แล้ว

    Good

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว

      Thanks

  • @nazirahmed99
    @nazirahmed99 4 ปีที่แล้ว

    Very helpful 😊

    • @KOMATH
      @KOMATH  3 ปีที่แล้ว

      Glad it was helpful!

  • @aemichohan4031
    @aemichohan4031 4 ปีที่แล้ว

    The great vedio

    • @KOMATH
      @KOMATH  4 ปีที่แล้ว

      Thanks!

    • @aemichohan4031
      @aemichohan4031 4 ปีที่แล้ว +1

      @@KOMATH most welcom😊

  • @johnraycardenas4711
    @johnraycardenas4711 3 ปีที่แล้ว +1

    Nice

  • @harimohan2255
    @harimohan2255 4 ปีที่แล้ว +1

    Thank you very much sir i watch just 1st one and i am able to solve my problems ❤️

    • @KOMATH
      @KOMATH  4 ปีที่แล้ว +2

      Glad to help!