Ratio test | Series | AP Calculus BC | Khan Academy

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น • 55

  • @caseycrown5069
    @caseycrown5069 4 ปีที่แล้ว +20

    "this isn't some voodoo" actually made me laugh out loud. Love you Sal!

  • @cagneymoreau4216
    @cagneymoreau4216 4 ปีที่แล้ว +15

    sal: this isn't voodoo
    everyone: actually it is

  • @NotoriousJ
    @NotoriousJ 7 ปีที่แล้ว +38

    6:45 "yes we can" sounded like Obama lol 😭

  • @krishnashah6667
    @krishnashah6667 4 ปีที่แล้ว +4

    Thank u so much....Now i can literally Visiulize the Seriea🤩🤩♥️

  • @RiaziMohandesi
    @RiaziMohandesi 2 ปีที่แล้ว +3

    What about harmonic series? It's a divergent series. 1+ 1/2 + 1/3 + 1/4 .....

  • @najeebkaraye5423
    @najeebkaraye5423 6 ปีที่แล้ว +7

    tank you very much sir,
    you make it easy to understand.

  • @owenzhu4497
    @owenzhu4497 3 ปีที่แล้ว +7

    how many of you watching this in college

    • @zachcrab5650
      @zachcrab5650 ปีที่แล้ว

      paying how much a year for the teachers to show me this and TAs to help more

  • @8bw
    @8bw 9 ปีที่แล้ว +9

    You can't prove that n^10/n! doesn't diverge with the divergence test as stated in 2:40 because lim an = 0 so it can still diverge ou converge. Or am I wrong?

    • @choff3102
      @choff3102 6 ปีที่แล้ว

      Correct, divergence test is inconclusive!

    • @ronelalday2472
      @ronelalday2472 4 ปีที่แล้ว

      Yes, divergence test has only two possible ending: the series diverges or the test is inconclusive.
      Divergence test cannot be used to prove the convergence of a series.

    • @kantarro671
      @kantarro671 3 ปีที่แล้ว

      You are right. For this video on the official website, there was a comment block that appeared right when he said it that wrote "The divergence test cannot be used for this case".

  • @erikmoe4767
    @erikmoe4767 6 ปีที่แล้ว +1

    Shoutout to Ms. Swish! Loved your PE classes. Keep on surfin' and catchin' those mavericks!

  • @einar5172
    @einar5172 2 ปีที่แล้ว +1

    Very useful! Thanks!

  • @farhansyed1038
    @farhansyed1038 10 ปีที่แล้ว +3

    Can you make videos on English like vocabulary and grammar

  • @StreetboyOfficiel
    @StreetboyOfficiel 7 ปีที่แล้ว +2

    Thanxs yall are genius

  • @aiicwyt6768
    @aiicwyt6768 7 ปีที่แล้ว +2

    Shoutout to Mr. Achille’s class!

  • @ChaminduHirushan-d2y
    @ChaminduHirushan-d2y 9 วันที่ผ่านมา

    thank you very much

  • @ismaelnaruto30
    @ismaelnaruto30 7 ปีที่แล้ว +4

    I love you man

  • @DeannaBoneman
    @DeannaBoneman 10 ปีที่แล้ว +2

    Do you have videos that teach like other subjects a and languages?

    • @martyspandex
      @martyspandex 10 ปีที่แล้ว

      They do. All the videos are on khanacademy.com. I suggest following the playlists.

    • @DeannaBoneman
      @DeannaBoneman 10 ปีที่แล้ว +1

      Thank you so much!!! martyspandex

    • @mohamedisaaq849
      @mohamedisaaq849 9 ปีที่แล้ว

      +deanna boneham yes

  • @leguminosa9
    @leguminosa9 8 ปีที่แล้ว +3

    what happen if the limit of (n+1)th term over nth term doesn't approach to any value? We simply cannot use Ratio Test, can we?

    • @Bignic2008
      @Bignic2008 7 ปีที่แล้ว +2

      Zerobyte Johnsons That's right. Using the ratio test requires that the limit actually exists and is a finite number.

    • @leguminosa9
      @leguminosa9 7 ปีที่แล้ว

      thx dude, just wanna clarify.

  • @amanmahendroo1784
    @amanmahendroo1784 7 ปีที่แล้ว +1

    1:40 I feel that if abs(r) = 1, the series STILL converges to the first term

    • @Litt13F00t
      @Litt13F00t 5 ปีที่แล้ว +6

      I realize this is from 2 years ago so apologies for bringing it up now as its probably not relevant for you anymore, but I thought it was still a question that deserved an answer- more for the sake of anyone who's reading these comments now with similar questions.
      If the ratio is 1, the sequence of terms would most certainly all be the same as the first term (since we're just multiplying by 1 each time), but what we mean when we talk about the convergence or divergence of a series is the *sum* of all of those terms. If the terms aren't approaching 0 as n --> infinity, then that sum can't be a finite number since you'll be continually adding new numbers to it (this is the idea behind the Divergence Test). In our case with r = 1, you're adding the same term over and over forever, so of course that infinite sum could only be written as being "equal" to infinity (in other words, it is a divergent series since the sum does not get closer and closer to equaling some finite number).
      Basically, what you've pointed out is that the *sequence of terms* "converges" to the first term as n --> infinity, but this is different from the series converging to a finite number (which, as the Divergence Test will show, can only occur if that sequence of terms goes to 0 as n --> infinity.

    • @Litt13F00t
      @Litt13F00t 4 ปีที่แล้ว +1

      @UCM74r8Kt9bGF4XPA61iFfVw I'm so glad it was helpful for you! It's definitely one of those things that I was incredibly happy to figure out for myself, I remember it being a big deal for me when that concept started to click. Are you in Calc 2 by any chance? Just curious, since that's where I was first introduced to this stuff (last semester for me)

    • @krishnashah6667
      @krishnashah6667 4 ปีที่แล้ว

      I guess =1 can be a different case...but definately that tends to infinity thts why Divergent suits the more

    • @krishnashah6667
      @krishnashah6667 4 ปีที่แล้ว +1

      @@Litt13F00t 🙏♥️

  • @maerkforbes786
    @maerkforbes786 9 ปีที่แล้ว +30

    In every Khan academy video he verbally repeats any text he is writing several times and it drives me fucking crazy

    • @freechoas
      @freechoas 7 ปีที่แล้ว +31

      I don't even care about how many times he repeats himself, his teaching is absolutely astonishing

    • @adbasdbasdkasdja7246
      @adbasdbasdkasdja7246 7 ปีที่แล้ว +6

      it helps to stuck infos to our brains. its annoying as shit and i remember all of them because i was angry at that moment.

  • @abdullahsiddiquesiddique980
    @abdullahsiddiquesiddique980 ปีที่แล้ว

    Tell me k hmy kesy pta chly ga k is question ma kon sa test use hona hy?

  • @fish7455
    @fish7455 2 ปีที่แล้ว +2

    L + ratio

  • @rashmikababajee3328
    @rashmikababajee3328 6 ปีที่แล้ว +2

    how do we decide when to write n=5, n=1 or n=0? I am kind of confused :S

    • @peanuts8437
      @peanuts8437 5 ปีที่แล้ว +1

      it's given to you, becomes part of the question. Most will start at n=1 or n=0 for simplicity in finding a few initial terms

  • @Ari-xh6nr
    @Ari-xh6nr 3 ปีที่แล้ว

    Can’t watch this man at less then 2x speed lol

  • @sangamesh2727
    @sangamesh2727 2 ปีที่แล้ว

  • @cmdrbobert9862
    @cmdrbobert9862 3 ปีที่แล้ว

    I'm afraid I still cannot tell what it happening when you say that n is going to infinity. If n becomes infinity in both the denominator and the numerator of a fraction, isn't it just going to converge at 1 regardless?

    • @liorschifrin
      @liorschifrin ปีที่แล้ว +1

      Working with infinity and limits is weird, but basically the way it works here is the denominator in this case “approaches infinity faster” than the number are because it is a higher power. For example lim of n/n^2 approaches 0 because the denominator has a higher power. You can solve this by dividing the top and bottom by the highest power, so it would be come 1/n. And the lim as n approaches infinity of 1/n is one over a really big number which approaches 0

  • @tinotendafortune5481
    @tinotendafortune5481 7 ปีที่แล้ว +2

    une swag

  • @pepsico815
    @pepsico815 8 ปีที่แล้ว +1

    I thought the ratio of a geometric series was An/An-1?

    • @obama8mychickenz
      @obama8mychickenz 8 ปีที่แล้ว

      no, it is a1/(1-r)
      and r is the common ration between terms

    • @krishnashah6667
      @krishnashah6667 4 ปีที่แล้ว

      Just the same....Succeeding term divided by Preceding Term

  • @DmitriNesteruk
    @DmitriNesteruk 10 ปีที่แล้ว +4

    You might want to consider avoiding the hand as the pointer - it is severely distracting!

  • @Gaemanino9
    @Gaemanino9 7 ปีที่แล้ว +2

    Prof. Leonard > Khan academy

    • @arsenron
      @arsenron 6 ปีที่แล้ว +3

      Prof. Leonardo + Khan good mix

    • @JohannSuarez
      @JohannSuarez 5 ปีที่แล้ว +1

      Or just learn from both.

  • @davidflores6363
    @davidflores6363 10 ปีที่แล้ว +7

    sexy voice'