Alternating Series Estimation Theorem

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  • เผยแพร่เมื่อ 23 ธ.ค. 2024

ความคิดเห็น • 153

  • @djohns71095
    @djohns71095 12 ปีที่แล้ว +32

    Dude...I have an associates in science and am currently double majoring in petroleum engineering and biochemistry with a chemistry minor. With that being said, I would like to thank you for helping me achieved what I have during my studies thus far. I've watched your videos for a long time now and have never shown my appreciation. You are a fucking awesome person!

  • @VinOnline
    @VinOnline 2 ปีที่แล้ว +5

    It's weird this math existed in 2008. Obviously it's not werid. But. I was so young at the time, it's like this math was lurking in the shadows waiting for me to go to college then attack me. But your videos are very helpful and serve as a good defence against this monster.

  • @gizlibahcem4408
    @gizlibahcem4408 11 ปีที่แล้ว +6

    You are my Math God! I can not describe how I feeling, I'm a student of METU, in first exam I got 41. and then 1 day before my second midterm, I found your channel I watched videos as much as I can and I got 71-curve of the exam is 46- thanks a lot thanks a lot.. much love from Turkey Pat:))

  • @jingyiwang5113
    @jingyiwang5113 2 ปีที่แล้ว +2

    Thanks so much for your patience in explaining the approximation of the sum of the alternating series so clearly. I have been puzzled with the way my textbook explains it for such a long time. I am so grateful for your help!

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว +5

    glad you like my videos :) come back often!

  • @RipcordHQ
    @RipcordHQ 13 ปีที่แล้ว +4

    I just found your videos, Great work man!
    I'm studying for my calc 2 test tomorrow and the only thing I didn't understand was this estimation theorem. (missed that class)
    Now I get it and I'm confident for my test. Thanks!

  • @klayworldsniper
    @klayworldsniper 13 ปีที่แล้ว +1

    I have a test in an hour and didn't understand this stuff. Now I do. Thanks so much, you're my pre-test ritual.

  • @love2CUsmile86
    @love2CUsmile86 16 ปีที่แล้ว

    Thank you so much! I'm currently taking Calculus. My teacher is nice but her teaching style is not simple as yours. She teaches to get the lesson done so she can get her paycheck, not because she wants use to truly learn math. I visited your website and it helps A LOT. You made it so much easier. Thank you.

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @fhunkymonkey no, taylor's theorem does not work that way; it is a bit more complicated

  • @marinocommapaul
    @marinocommapaul 12 ปีที่แล้ว +1

    also your examples are perfect. concise, yet covering a broad range of ideas. really stellar stuff Pat keep it up. many thanks

  • @junaidkhan4564
    @junaidkhan4564 4 ปีที่แล้ว

    You've won the day bro. I've looked upto khan academy and The Organic Chemistry Tutor , but nobody made any sense instead you did. Thanks.

  • @xrockerchick4lifex
    @xrockerchick4lifex 13 ปีที่แล้ว +1

    This was soooo helpful! I was stuck on a problem like this for a half hour and you saved me in 30 seconds!!

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @iammaxhailme well, this only works for alternating estimation theorem

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว +2

    ahhh ok, it is conditionally convergent : )
    in many books, when one first learns about alternating series, you do not yet know about absolute/conditional convergence, so i figure it would just confuse people to throw that terminology in there at that point

  • @zachb9440
    @zachb9440 ปีที่แล้ว

    best explanation of this theorem on TH-cam - thank you man

  • @emoster7195
    @emoster7195 6 ปีที่แล้ว

    so clear and straightforward! your videos play right into my learning style of annotated exercises and i can replay this at my own pace! unlike in the lectures

  • @astrobiologist
    @astrobiologist 14 ปีที่แล้ว +1

    Thanks for the good review. We have an exam tomorrow in Calc 2 on infinite series. I've been trying to find information on how to determine whether the error for an alternating series estimation is an overestimate or an underestimate...

  • @erickpeculiar823
    @erickpeculiar823 4 ปีที่แล้ว

    your videos are so good. Short and direct to the point

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว +1

    ha! god of math! not quite, but i appreciate the nice words all the same! good luck on your midterm!!

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @FaiththeHairstylist yep, and it makes total sense!

  • @heatherkeightly8611
    @heatherkeightly8611 11 ปีที่แล้ว

    You teach incredibly better than my math professors. Thank you so much for the videos!

  • @mbs5014
    @mbs5014 9 ปีที่แล้ว +30

    how can I do exercises like this without a calculator!!? because it isn't allowed in exam

    • @johndemitrios6063
      @johndemitrios6063 7 ปีที่แล้ว +4

      you add fractions manually

    • @AA-ht3ce
      @AA-ht3ce 7 ปีที่แล้ว +3

      you must be a student in CSU ha!

    • @321Leviathan
      @321Leviathan 6 ปีที่แล้ว +3

      Well I'm assuming you already took the exam, but they likely would not put anything too crazy on an exam that wouldn't require a calculator

    • @anavsingh2794
      @anavsingh2794 6 ปีที่แล้ว

      Calc 2 at UVA is also done without a calculator but the professors know and go easy on the calculations.

  • @Chocoholic319
    @Chocoholic319 12 ปีที่แล้ว

    Watching your videos is WAYYYYYY more productive than listening to my prof - Thank you, your website is amazing! XD

  • @elilawrence2567
    @elilawrence2567 8 ปีที่แล้ว

    really helpful man! I missed this lecture in class and would have been completely lost without this vid

  • @goopop67
    @goopop67 12 ปีที่แล้ว +1

    thanks to your videos I probably got an A on my last exam
    You deserve my tuition

  • @herochengify
    @herochengify 10 ปีที่แล้ว

    The best teacher created the best videos!

  • @dannydsc7
    @dannydsc7 11 ปีที่แล้ว

    How do you it? You make it so much clearer and easier than James Stewart and my calc professor. Real talk - you should be sainted. "Saint Patrick JMT." Saint of mathematics.

  • @chocochris93
    @chocochris93 13 ปีที่แล้ว

    your videos are now an essential part of my studying. Thank you very much!

  • @robertoberidojr.435
    @robertoberidojr.435 3 ปีที่แล้ว

    This is 12 years ago and still so useful

  • @marinocommapaul
    @marinocommapaul 12 ปีที่แล้ว

    this is extremely clear you must be a great math tutor!

  • @patrickjmt
    @patrickjmt  13 ปีที่แล้ว

    @geebauer just doin' what i can

  • @jasonjkeller79
    @jasonjkeller79 13 ปีที่แล้ว

    Is it correct to assume that this will work for an alternating power series as well, given a situation where we know what n and x equal?

  • @tinazheng892
    @tinazheng892 5 ปีที่แล้ว

    Why is it four zeros for four decimal places? Would it be three zeroes instead since it's accurate to the 4th decimal places?

  • @buttman20
    @buttman20 15 ปีที่แล้ว

    Thank you, your instructions are clear and coherent! It makes perfect sense, and I definitely understood this at an applicable level!
    Be my teacher!

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว +2

    hey! a 'B' is good! nice job! : )

  • @spougatc1
    @spougatc1 11 ปีที่แล้ว

    whats up Patrick,
    Im stuck on a series problem and would like to know what video you can direct me to not to solve this particular problem but just to understand the concept and approach.
    The problem is:
    SUM for n=1, to infinity of 4/(4n-3)(4n+1)

  • @Soul_Revenant
    @Soul_Revenant 11 ปีที่แล้ว

    This method and explanation has helped me a lot as with all of your other videos. But when I tried this method with arctan(0.5) to 3 decimal places it tells me that rejecting the 5th term will give me the desired accuracy but that gives me 0.463 and the correct answer is 0.464. I was wondering if I could get some help with this as I have a final coming up really soon. Thanks.

  • @goldenotis9703
    @goldenotis9703 6 ปีที่แล้ว

    Thank you this is really helpful. But what of when N is really big is their a way to sum up Sn without doing the addition by hand? and here is the specific problem I'm working on ∑n=1∞(−1)n+1(n+2)(n+10) with an error of at most 10^-3.

  • @BaoNguyendarkmatter820
    @BaoNguyendarkmatter820 13 ปีที่แล้ว

    Hi Patrick. If I want to solve it algebraically, and within 0.001, do I set a of n equal to 0.001? Thanks

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    thanks and thanks!
    you going to study math in college?

  • @AlphaSquadZero
    @AlphaSquadZero 11 ปีที่แล้ว

    Really helpful stuff even when I am solving the reverse sort of problem (given an error, but need to find interval of x).

  • @koreahiho
    @koreahiho 13 ปีที่แล้ว

    Hi Patrick. If you don't mind could you help me please?
    So I have to find 3 diffrent values of u
    ( (-1) ^n * (1/(1-u))* 4n ) / (2n)! = -1/2
    I tried to do with estimation...but I have no idea...
    then I tried to do limit comparaison, but it does not tell me the sum of the series.
    or should I use Taylor theoreme?
    Please I am literally begging you how to solve this.
    Thank you

  • @icono__7136
    @icono__7136 4 ปีที่แล้ว

    waited 6 mins of my life (because that's when I noped out). You're explaining this concept in a very snake-oil selling way

    • @patrickjmt
      @patrickjmt  4 ปีที่แล้ว +1

      i have no idea what you are trying to say

  • @siriusblack9999
    @siriusblack9999 14 ปีที่แล้ว

    actually i noticed something with the second example here, apologies if this was already mentioned or if it's an invalid argument
    but the 6th term would add 0.000023... to 0.098785...
    that makes the new number 0.098808, with the next number substracting some part(probably smaller than 0.00001), so the 4th decimal is actually incorrect

  • @sardarazimov3944
    @sardarazimov3944 8 ปีที่แล้ว

    the best teacher ever!Thank you!!!

  • @Isou3008
    @Isou3008 12 ปีที่แล้ว

    Some teachers need to see your videos before going to class.

  • @itskyleeeeeee
    @itskyleeeeeee 5 ปีที่แล้ว

    "Otherwise, it doesn't make any sense that you are talking it". love that line haha

  • @AmandaBear2010
    @AmandaBear2010 11 ปีที่แล้ว +5

    thanks for your help!! I just got a 98% on my last calc II exam

    • @011vikes
      @011vikes 11 ปีที่แล้ว +4

      98?? that's good. i have a calc II midterm tomorrow..taylor/mclaurin/series tests/vectors

    • @grantdennany7602
      @grantdennany7602 6 ปีที่แล้ว

      im sorry congratulations

  • @blink11101
    @blink11101 11 ปีที่แล้ว

    although it is a brute force technique, your way makes more sense than the way we went over in class.

  • @patrickjmt
    @patrickjmt  15 ปีที่แล้ว +1

    near perfect sounds quite alright to me : )

  • @brco2003
    @brco2003 16 ปีที่แล้ว

    were you doing those 8-powers in your head or calculator?

  • @hen555
    @hen555 13 ปีที่แล้ว

    learned this in 10 minutes what wud actualy take 1 hour if i tried learning from the book.
    thanks!

  • @emanuelcadillac
    @emanuelcadillac 11 ปีที่แล้ว

    how do find b(n) :( im confused. i get the rest of the video but i just don't get it that one part.

  • @TheEdwards56
    @TheEdwards56 11 ปีที่แล้ว

    Thank you so much for explaining this Pat. You're great!

  • @alannahdzijacky4543
    @alannahdzijacky4543 10 ปีที่แล้ว +11

    how would you do this if you weren't allowed a calculator on a final exam...

    • @DannyStopMotions
      @DannyStopMotions 9 ปีที่แล้ว +5

      You would probably not be asked something like this without a calculator. If you are, just leave it as fractions to show you know HOW to do it.

  • @TheShortboy333
    @TheShortboy333 11 ปีที่แล้ว

    Isn't 1/n the divergent harmonic series?

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @cacaloveforever i have gone back to the sharpie and paper

  • @harrisonbrewer8786
    @harrisonbrewer8786 10 ปีที่แล้ว +4

    YOU ARE BAE. Thank you so much!!

  • @ayanaxhye
    @ayanaxhye ปีที่แล้ว +1

    mates a genius

  • @annafeting9741
    @annafeting9741 5 ปีที่แล้ว

    Great explanation! Thank you

  • @purcell2319
    @purcell2319 5 ปีที่แล้ว

    I was a little pissed to hear that you wouldn’t offer a rigorous algebraic explanation of how to solve the inequality error_n < T, where T is a given threshold. But after working a bit on my own I have realized that it’s kind of brutal to get to that kind of surefire method, this outweighing the simplicity of brute-forcing it. However, for crazy thresholds or whatever one would like to call it, I think it’s probably best to work the inequality algebraically until there’s something simpler to brute-force

  • @ronniemonnie
    @ronniemonnie 13 ปีที่แล้ว

    Wait... how do you know which term is the first neglected term?

  • @3Daybreaker
    @3Daybreaker 14 ปีที่แล้ว

    Thank you so much for your videos. Great for quick review!

  • @rochelleroberts5837
    @rochelleroberts5837 11 ปีที่แล้ว

    What would the inequalities look like?

  • @tadradtad
    @tadradtad 12 ปีที่แล้ว

    Is it possible to solve these algebraically?

  • @MrBlash93
    @MrBlash93 10 ปีที่แล้ว

    thanks PatrickJMT

  • @cubanjr2
    @cubanjr2 11 ปีที่แล้ว

    great videos man, helps a ton!

  • @veronicathen9157
    @veronicathen9157 5 ปีที่แล้ว

    thanks a lot this method is quick and easy

  • @waleed.junaidy
    @waleed.junaidy 11 ปีที่แล้ว

    Could you solve this algebraicly aswel as we are not allowed a calculator on our exams? Thanks :)

  • @iammaxhailme
    @iammaxhailme 14 ปีที่แล้ว

    @patrickJMT
    I was expecting either an alternate estimate or an integral estimate to show up on my exam (that I took between my last comment and this one) but it didn't anyway

  • @Thanan11
    @Thanan11 11 ปีที่แล้ว

    1/n is a divergent harmonic series but (-1)^n 1/n is not, using the alterning series test

  • @chrisv7892
    @chrisv7892 10 ปีที่แล้ว

    oMG that is so easy. I almost shut you off when i saw that first 15 seconds of mumbojumbo. e tu patric e tu? That should come after the easy train

  • @icpark
    @icpark 15 ปีที่แล้ว

    In the first example, he added a +1 to the ^n, making his signs right. (at 2:05)

  • @emanuelcadillac
    @emanuelcadillac 11 ปีที่แล้ว

    Never mind i got it T_T i just had one of those moments... BUT awesome vid. real life and time saver...

  • @thesprittany
    @thesprittany 10 ปีที่แล้ว

    Thanks so much! It was really helpful.

  • @patrickjmt
    @patrickjmt  12 ปีที่แล้ว

    thanks! :)

  • @olivianetzler3031
    @olivianetzler3031 6 ปีที่แล้ว

    Thank you, Sir!

  • @임혜민-l3u
    @임혜민-l3u 5 ปีที่แล้ว

    thank you so much you helped me a lot

  • @andreariballo2207
    @andreariballo2207 12 ปีที่แล้ว

    Thank you... i wish you were my teacher

  • @23youwatch
    @23youwatch 14 ปีที่แล้ว

    u are the BEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  • @tommykho2256
    @tommykho2256 10 ปีที่แล้ว

    Aren't you should add the term with four zeros as well?

  • @MRAXELGRINDER
    @MRAXELGRINDER 5 ปีที่แล้ว

    Great video!!! Thank you

  • @patrickjmt
    @patrickjmt  14 ปีที่แล้ว

    @ShivMan007 ha, thanks : )

  • @angeljohn1250
    @angeljohn1250 8 ปีที่แล้ว

    god bless you patrick

  • @geebauer
    @geebauer 13 ปีที่แล้ว

    Youre a boss Pat

  • @LapinAngelique00
    @LapinAngelique00 11 ปีที่แล้ว

    If you go to 1:33 in the video, he shows that the (-1)^n is what makes it an alternating series and the other part is your b(n)

  • @akosiredred
    @akosiredred 12 ปีที่แล้ว

    i click on most of yer vids to add up to the views. my way of saying thanks. :))

  • @TheCj383
    @TheCj383 12 ปีที่แล้ว

    Pat... You are my Homie.

  • @cutcub
    @cutcub 15 ปีที่แล้ว

    Thank you

  • @purcell2319
    @purcell2319 5 ปีที่แล้ว +2

    Dude, I’m pretty sure you’re still active, so hopefully you’ll update this with an algebraic example. This brute force method isn’t that helpful when the bound is something weird like 7/5^7 or sqrt(pi)

  • @fiorellavt1
    @fiorellavt1 16 ปีที่แล้ว

    thanks! it is clear now

  • @itheblackwolfofmyfamily
    @itheblackwolfofmyfamily 5 ปีที่แล้ว

    thank you so much

  • @kendragonzalezduran5079
    @kendragonzalezduran5079 8 ปีที่แล้ว

    Thank you so much!!!

  • @johndemitrios6063
    @johndemitrios6063 7 ปีที่แล้ว

    well done!

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    did i say something different - i do not want to watch it all and find it out

  • @patrickjmt
    @patrickjmt  16 ปีที่แล้ว

    ha! thanks : )

  • @christopherjackson29
    @christopherjackson29 7 ปีที่แล้ว

    Tyvm

  • @steveofreeblind
    @steveofreeblind 16 ปีที่แล้ว

    you are amazing

  • @evanmargolis8468
    @evanmargolis8468 9 ปีที่แล้ว +15

    Why does this have any dislikes

  • @toastedmarshmellow704
    @toastedmarshmellow704 6 ปีที่แล้ว

    lim n->inf i/n = 0 because 1/n becomes so small and approaches zero