Geometric Series and the Test for Divergence - Part 2

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  • Опубликовано: 21 янв 2025

Комментарии • 115

  • @lifematch
    @lifematch 15 лет назад

    patrick i have been watching ur videos from limits to here. I pretty much learned calculus from your video rather then the text book and prof. Don't like to admitted but i skip my math class all the time cuz your video are much better then my prof's lecture. Your video has been a huge asset in my life! i would like to take this chance to wholeheartedly thank you for everything you have done for us. Please keep what your doing best and hope all your life problems will be solved (if any)!

  • @Halo19852
    @Halo19852 11 лет назад +1

    thank you so much, I've watched nearly 20 of your videos just today to study for my AP calculus test, you explain everything very clearly, you are saving my grade!

  • @layton723
    @layton723 9 лет назад +45

    for the answer, the first part converges to 1, but the second part converges to 1/2 not 2. so the final answer is 3/2 or 1.5 not 3

    • @huizylove
      @huizylove 3 года назад

      but does it converge? because the summation is 1.5? or the converges are tested one by one and then we have the total summation?

    • @nicollassdossantos
      @nicollassdossantos 2 года назад

      @@huizylove We know both series converge because in both cases we have -1 < r < 1. And we split in two series, so we consider the total summation (the value the first one converges to plus the value the second one converges to).

  • @robotMETALBOMB
    @robotMETALBOMB 12 лет назад +1

    thank you so much. i know you hear it all the time but you are truly one of the easiest people to learn from. you're awesome
    -sincerley, everyone who's ever taken calculus

  • @patrickjmt
    @patrickjmt  14 лет назад

    @jhh1822 ops yes, my mistake!

  • @eviltwin1000
    @eviltwin1000 15 лет назад

    You are a fantastic teacher! Many professors are doctors, etc, but they're not meant to teach! You make things a lot simpler and make math fun!

  • @BenAp45
    @BenAp45 12 лет назад

    I have struggled with learning calculus at UCLA until finding your videos. You teach these concepts very simply and show every step along the way. I wish more of my teachers taught like you. Thank you!!!

  • @tpubill
    @tpubill 14 лет назад

    you are a much better teacher than my current calc II teacher. you make series seem so easy. so thank you so much. you're a life saver :D

  • @patrickjmt
    @patrickjmt  14 лет назад

    @DashofDosh ha - now i feel pressured to make good videos!

  • @armin458s
    @armin458s 11 лет назад

    The forms you put your equations in were spot on with the summations I needed to figure out. Thank you!

  • @GallusSapien
    @GallusSapien 8 лет назад +47

    2:00 1/3 over 2/3 is 1/2 not 2

  • @patrickjmt
    @patrickjmt  14 лет назад

    @mosum91 you are welcome

  • @DashofDosh
    @DashofDosh 14 лет назад

    thank you patrick! I treat calculus class as a free period but learn at night when I watch your videos.

  • @TheMrlightswarm
    @TheMrlightswarm 12 лет назад +1

    TOO AWESOME THANKS! I'm that way too, I can't compute simple math on demand, but I can grasp challenging concepts quickly.
    Interestingly enough, the series concepts aren't easy when being self-taught.

  • @ReneUlloa74kg
    @ReneUlloa74kg 8 лет назад +19

    MVP MVP MVP

  • @bmazymei
    @bmazymei 13 лет назад

    Even though I got a 37 on my exam before my final because my professor is a pompous prick with a 50% pass rate, watching your videos helped me ace the final and pull out with an A in my calc 1 class, thanks so much!

  • @TanvirKawnine
    @TanvirKawnine 13 лет назад

    Thanks Patrick, your videos are great help for me to understand calculus.

  • @patrickjmt
    @patrickjmt  14 лет назад

    @DonChedda opppps! i am just making sure you all are paying attention

  • @DareBear808
    @DareBear808 11 лет назад +1

    Thank you for you very informative videos. You break the concepts down so well that it is very easy to understand the concepts.

  • @patrickjmt
    @patrickjmt  13 лет назад

    @The1ntern well, math videos seem like a good place to advertise math videos : )

  • @nellyk5884
    @nellyk5884 11 лет назад

    Dude you are awesome..i've got this cal teacher who doesn't know how to teach -.- my final is tomorrow, u just helped me regain my confidence.. (:

  • @koerbemd
    @koerbemd 14 лет назад

    Patrick, I don't know if someone has mentioned this, but is (1/3)/(2/3)= .5, and it would diverge to 1.5... Unless I made a stupid mistake somewhere, which is 100% possible. Thank you so much for the videos though. I use your videos more than my lecture. Calc 2 midterm t-minus 16 hours.

  • @43510dude
    @43510dude 7 лет назад

    Haven't been to class all year and this basically summed up a 2 week unit into 5 minutes

  • @patrickjmt
    @patrickjmt  12 лет назад

    glad you like them! thanks a bunch for spreading the word!!

  • @caoq6876
    @caoq6876 12 лет назад

    I have midterm tomorrow. your videos really help me. thanks a lot

  • @tamerachristopher6002
    @tamerachristopher6002 8 лет назад

    You're The best Patrick!!! really saving my life right now!!!

  • @tonytran6264
    @tonytran6264 11 лет назад

    I have a question! Since the geometric series state that the formula should be in this form.... ar^(n-1).... wouldn't you need to change it?

  • @Fonseca1492
    @Fonseca1492 11 лет назад +2

    You save my life. I had difficult times with this topic. I got the basic concept now. :-)

  • @duskshadowbrony
    @duskshadowbrony 11 лет назад

    How do I tell the difference between a P series and a Geometric series? My professor also said something about alternating series, but she mumbles and uses markers almost out of ink, so my notes are pretty much useless.

  • @patrickjmt
    @patrickjmt  14 лет назад

    @Tweak2727 a big 'your welcome' to all the unlv students!

  • @Billabong024
    @Billabong024 13 лет назад +1

    freakin awesome dude. I just learned this thing today and you make it so much easier.
    Also I got a 100 on my 2nd test on integration!
    Thank you

  • @FrigginSmift
    @FrigginSmift 13 лет назад

    I learn more in one of your 5min vids than i do in my 2hr lectures

  • @a7a89
    @a7a89 12 лет назад +1

    what is exactly should be reconsidered? 1/3 divided by 2/3 equal 1/2 and 1+1/2=3/2 ???!!!!!!!!!

  • @stanleychu4107
    @stanleychu4107 10 лет назад +15

    you saved me. you have no idea. thank you. so much. soso much.

  • @sebaninayak1611
    @sebaninayak1611 7 лет назад

    which one is the very first vdo to learn convergence and divergence of an infinite series?

  • @TOYOTER0
    @TOYOTER0 12 лет назад

    Link to the first part please? :-D

  • @Agustinoism
    @Agustinoism 11 лет назад

    Your math videos help a lot you are a boss.

  • @mnstrgdflla
    @mnstrgdflla 16 лет назад

    how does that answer the question?

  • @vedavarma5358
    @vedavarma5358 7 лет назад +1

    I just wanted to check if the series converges or diverges....so I applies limit tends to infinity to the function. I just got log (6^6^n)/log(6^6^n) = 1 which is not equal to 0. So the series diverges.... But actually the series converges.... Can somebody help me on this....

  • @moonflash007
    @moonflash007 12 лет назад

    using the test for divergence , (1/2)^n for n->oo is equal to 1 , which is not equal to 0 ! so why does (1/2)^n converge and not diverge?

  • @lucasargandona4658
    @lucasargandona4658 4 года назад

    I thought geometric series had to be in the n-1 format and the only way to do the ^n way, the sigma below has to equal 0?

  • @ARTDEVGRU247
    @ARTDEVGRU247 2 года назад +1

    the second series was 1/2, not 2.

  • @UzumakiNaruto-xt9fm
    @UzumakiNaruto-xt9fm 6 лет назад

    you are the man who saved my life!!!!!!!!!!!!!!!!!!

  • @linocutter
    @linocutter 13 лет назад

    ugh.. why didn't I watch these videos earlier in the semester.. !!
    If I did, I would not be stressing so much about the final and I would definitely end up with an A in my Calc II class

  • @mightykristenvideoprojects8784
    @mightykristenvideoprojects8784 8 лет назад

    I thought you can only do the (a/(1-r) if (n-1)? I'm confused.

    • @dahazz
      @dahazz 8 лет назад

      +Kristen Henderson You can only use 'that' (which is the sum of a given geometric series). If r is a number which is less than one (regardless of positive or negative sign). Example, 2/3, 4/5. All are less than one. So, we evaluate one of these numbers from a given limit, hoping to get a fraction which is less than one. So we use that as our r and find a by plugging in the inital value of n which they specified to start with (like n=1). If we don't get a number which is less than one, then the series is divergent and a sum for that series, does not exist.

  • @patrickjmt
    @patrickjmt  14 лет назад

    @like9orphanz perfect : )

  • @Enerjikk
    @Enerjikk 12 лет назад

    yay! it should be reconsidered pat, all due respect

  • @dfts22e
    @dfts22e 14 лет назад

    Please make more sequences and SERIES videos!

  • @patrickjmt
    @patrickjmt  13 лет назад

    @Billabong024 good job!

  • @jtnorg
    @jtnorg 16 лет назад

    wait....(1/3)/(2/3)=(1/2) correct. so doesnt it converge to (3/2)

  • @Ammm649
    @Ammm649 13 лет назад

    @linocutter same here my final is tomorow and this series driving me crazy

  • @eidsaw
    @eidsaw 8 лет назад

    why Term 1/2 ? and 1/3

    • @1_-Kira-_1
      @1_-Kira-_1 8 лет назад

      Bc it starts at n=1 so the first terms are 1/2 & 1/3

  • @alexrasidakis4584
    @alexrasidakis4584 10 лет назад +1

    On your previous video 'what is series' you said that the formula (a/(1-r)) works only if our common ratio is raised to 'n-1'... Here on your last example you used the formula even if the common ratio was raised to 'n'.. Did i understand something wrong or you just forgot it?... thanks by the way you helped me a lot ! :)

    • @sanizzhott
      @sanizzhott 8 лет назад

      yes this is confusing me and others as well....

  • @somayyaummnabil7617
    @somayyaummnabil7617 7 лет назад

    OMG THANK YOUUUUUUUU... Brilliant videos!

  • @100yearsofsolitudful
    @100yearsofsolitudful 11 лет назад

    thank you very much patrick

  • @sanizzhott
    @sanizzhott 8 лет назад

    wait... i thought you can only us a/(1-r) if the series is to the (n-l)power....

  • @mangaliewa
    @mangaliewa 13 лет назад

    how can you dislike a fucking good educational video? wtf

  • @The3jji
    @The3jji 14 лет назад

    The series converges to 1.5
    Please check if its correct :)

  • @mistersirisaacnewton
    @mistersirisaacnewton 12 лет назад

    if I ever become successful, I'll be sure to be making a very generous donation to your website for helping put me through college math

  • @VDEL279
    @VDEL279 12 лет назад +1

    I LOVE YOU

  • @Splashmaster97
    @Splashmaster97 7 лет назад

    i made the exact same mistake evaluating it... its at this point that we as people forget arithmetic...

  • @Enerjikk
    @Enerjikk 12 лет назад

    actually i was backing your idea, i said "pat" for patrick dude, sorry for confusion

  • @pointed8
    @pointed8 13 лет назад

    @mamatela As you can see yourself, everybody makes mistakes !

  • @gmkumo
    @gmkumo 10 лет назад +1

    THANKS A LOT

  • @bryanj12341
    @bryanj12341 15 лет назад

    cool videos!

  • @TheRainbow54321
    @TheRainbow54321 11 лет назад

    Thank you so much!!

  • @naylin369
    @naylin369 15 лет назад

    you forgot to flip the fraction when you divide. I think u got it wrong the answer is thus 3 not 3/2 please check again.

  • @pleaseletmeregister379
    @pleaseletmeregister379 11 лет назад +2

    To be honest i think your videos are easier to understand the khanacademy videos

  • @akomoje
    @akomoje 11 лет назад

    Thank you so much.

  • @a7a89
    @a7a89 12 лет назад

    It will converge to 3/2 not 3, because (1/3)/(2/3) = 1/2

  • @dillmon1
    @dillmon1 14 лет назад

    YES!! I actually understand this shit now!

  • @rongcc8855
    @rongcc8855 8 лет назад

    you did very well

  • @andreablacker
    @andreablacker 15 лет назад

    only because 1 elevated to anything gives you 1... if not you couldn't do that.

  • @annalydiaryan6505
    @annalydiaryan6505 8 лет назад

    Thanks Patrick! I love you so much! You're almost better than Khan!

    • @aroojishaq1591
      @aroojishaq1591 8 лет назад +4

      +anna lydia almost? wow that mustve hurt him

  • @waxbarashoschool4699
    @waxbarashoschool4699 6 лет назад +1

    Thanks but it converges to 3/2 not 3 otherwise nice video

  • @mounikasagi9460
    @mounikasagi9460 11 лет назад

    thanks a lot sir.

  • @bAdDA5z
    @bAdDA5z 10 лет назад

    why doesn't it converge to 0? you are raising a number between 0 and 1 to the power of infinity.

    • @SaiyanPowerZ
      @SaiyanPowerZ 10 лет назад +4

      series = sum. the final term at infinity will be 0 but if u add all the terms up to the infinite term u will end with the sum

  • @arousedacorn7454
    @arousedacorn7454 8 лет назад

    thank you!!

  • @danthemanpatrick
    @danthemanpatrick 13 лет назад

    help, thy name is patrickJMT

  • @edyraper
    @edyraper 7 лет назад

    Patrick for 2020

  • @aminanabeel9561
    @aminanabeel9561 7 лет назад

    You are greattttttt

  • @Petrrr33
    @Petrrr33 12 лет назад

    1/2^oo = 0 ,so is convergent

  • @EverydayXperiment
    @EverydayXperiment 12 лет назад

    I love you!!!

  • @teefinyomouf
    @teefinyomouf 11 лет назад

    is "bust up" a math term cause both you and my calc professor say it LOL

  • @Ledarifique
    @Ledarifique 15 лет назад

    Why are the cool and intelligent people always the ones to be left handed?

  • @bryanj12341
    @bryanj12341 15 лет назад

    yup

  • @willwen645
    @willwen645 11 лет назад +1

    i got 1.5 as my answer

  • @limbo060
    @limbo060 7 лет назад

    thx

  • @a7a89
    @a7a89 12 лет назад

    ooooh okay, sorry I misunderstood I feel like a dumb ass right now loool

  • @devadosantos4973
    @devadosantos4973 6 лет назад

    wow it was good

  • @rwiebster
    @rwiebster 15 лет назад

    sometimes i think they should start a youtube university.

  • @100yearsofsolitudful
    @100yearsofsolitudful 11 лет назад

    don't compare them, but i know what u mean :)

  • @2ndintelligentWorld
    @2ndintelligentWorld 12 лет назад

    i hate "that tutor guy"

  • @mamatela
    @mamatela 13 лет назад

    you're wrong...... ((1/3)/1-(2/3))= 3/2

  • @ArasmusInc
    @ArasmusInc 12 лет назад

    mine are of ebay :D

  • @Enerjikk
    @Enerjikk 12 лет назад

    haha, dont be:)

  • @aG_oh_so_Sneaky
    @aG_oh_so_Sneaky 3 года назад

    oh just kidding

  • @chopperwtfreed
    @chopperwtfreed 16 лет назад

    first view, cool

  • @joehu2667
    @joehu2667 10 лет назад +2

    this is wrong guys, you can't use this theorem if the series start from n=1, you have to change the series to start from n=0 and then use 1/(1-x).
    the answer for this question should be 1.5

    • @raggy6657
      @raggy6657 10 лет назад +9

      It's perfectly fine to do what he did, he simply did his arithmetic at the end wrong. he said (1/3)/(2/3) is equal to two instead of .5. Either way you do it, the answer is 1.5

    • @joehu2667
      @joehu2667 10 лет назад

      If it is for higher level math, we should use Theorem instead of the way he did it. The answer maybe right, but it won't get full point for it.

    • @raggy6657
      @raggy6657 10 лет назад +3

      Jiaqi Hu It was certainly accepted on my college Calc 2 final, though it is true that some professors may not accept it.

    • @alexrasidakis4584
      @alexrasidakis4584 10 лет назад +1

      check here.. you are right www.wolframalpha.com/widgets/view.jsp?id=86ceba9f35c96ebae137e44a36c7261a

  • @TOYOTER0
    @TOYOTER0 12 лет назад

    Link to the first part please? :-D