Using the Ratio Test to Determine if a Series Converges #1

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  • Опубліковано 2 кві 2008
  • Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Using the Ratio Test to Determine if a Series Converges or Diverges - Two examples are shown. In another video, two more examples are shown! For more free math videos, visit my NEW site PatrickJMT.com
    Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor

КОМЕНТАРІ • 392

  • @aelhkmm6009
    @aelhkmm6009 7 років тому +152

    There's a special place in heaven for people like you!

  • @aymansiam515
    @aymansiam515 4 роки тому +55

    I was like 8 when this came out, I'm 20 now LOL

  • @monicasarmiento987
    @monicasarmiento987 10 років тому +47

    2^n+1 can be simplified to 2^n * 2^1 which is how a two remains on the bottom

  • @patrickjmt
    @patrickjmt  15 років тому +11

    that is the fun part
    it is like integration - at first you do not know what to do, but then, after doing 80000 of them, you recognize some common traits.
    the same is true with series. you just have to get your hands dirty and try all sorts of things. eventually, you will recognize certain features that you clue you in to what might work.
    basically your question is like: given any math problem, how do i solve it?
    the question is just too broad!

  • @victoriabeck1763
    @victoriabeck1763 8 років тому +156

    Just wanna say thank you for not being one of those people who try to be over enthusiastic in there videos. I like that you are just normal haha!

    • @victoriabeck1763
      @victoriabeck1763 8 років тому +1

      +Victoria Menefee their*

    • @patrickjmt
      @patrickjmt  8 років тому +93

      Hard to be super excited about the ratio test :)

    • @johnlang555
      @johnlang555 8 років тому

      +Victoria Menefee shots fired

    • @johnlang555
      @johnlang555 8 років тому

      ***** your right bro

    • @humodedam5311
      @humodedam5311 7 років тому

      Victoria Menefee Thank Him really

  • @patrickjmt
    @patrickjmt  15 років тому +16

    nah, u are the one working hard and studying : )
    i am simply a recorded hand doing problems

    • @igxniisan6996
      @igxniisan6996 3 роки тому +1

      Damn dude, 12 years ago!
      These gives me nostalgia cuz the last time I was here with my old account was like 10 years ago (yeah true that I was only 8 so I didn't understand a single thing 😂)

  • @edris33
    @edris33 9 років тому +22

    You are better than a textbook, very nice work.

  • @quinnd3284
    @quinnd3284 8 років тому +5

    I know you probably get this a lot but I really appreciate all of your videos. It's been a busy school week for me and you're probably the only reason I'll manage to get a decent grade on my upcoming calculus exams. Thanks!

  • @Garen1234
    @Garen1234 16 років тому +1

    Man seriously, you deserve an award for how clearly you explain math! If you do a bunch of more examples like this and put it on a cd and sell it, I would buy it!

  • @965was
    @965was 8 років тому +39

    if any body asking how 4^n canceled with 4^n-1 ...
    look , 4^n-1 = 4^n . 4^-1
    so 4^n up canceled with 4^n down and remained 4^-1 which comes down to be 4

    • @cavendishop3962
      @cavendishop3962 8 років тому +1

      +abdullah albalushi lol I thought you asked the question so I was gonna give you an answer without reading the comment.

    • @LiveAventura
      @LiveAventura 7 років тому +2

      abdullah albalushi THANK YOUUUUU!!!! I've been stuck for like 2 hours trying to find out how tf it cancels out. Life saver !

    • @Monday97
      @Monday97 7 років тому

      abdullah albalushi جزاك الله خير يا البلوشي :)

    • @loquace95
      @loquace95 6 років тому

      abdullah albalushi you saved my life

    • @victorn3579
      @victorn3579 6 років тому

      But what if it was 4^+1 remaining on the bottom? Would it go to the top?

  • @Ortho_1_Christ
    @Ortho_1_Christ 14 років тому

    What a wonderful online teacher u r. This is amazing, I never see a calculus teacher this much organized. When I watch all what you doing it is crystal clear , and understandable. People like u really need some kind of support from the gov, as a sign of encouragment. U r supurp a million stars for u !! Thanks again for helpping ppl like me.

  • @BlessureK
    @BlessureK 15 років тому +2

    it took a while, but i finally understand this. thanks a heap for your videos again patrick. you helped me pass last semester, hopefully i can pass again

  • @patrickjmt
    @patrickjmt  15 років тому +3

    factorials !!!!! are often good problems to use ratio test on for sure...
    there are lots of problems ratio test works well for... sometimes you just get your hands dirty and try!

  • @patrickjmt
    @patrickjmt  15 років тому +1

    i have a few double integrals out there, but not much more at the moment!
    glad i could at least help out through series stuff! : )

  • @I3urningi3laze
    @I3urningi3laze 13 років тому

    Normally I get really pissed off when I see an advertisement on a video, but when I watch your videos, I feel proud to watch them because I know that it is a way for us, the viewers, to support your efforts!

  • @manirethnamganesan350
    @manirethnamganesan350 10 років тому +1

    Dude...u hv been helping me soo much for the past two semester......thank u very much....keep on doing more videos and help those in need out there.....
    :)

  • @Notsoskilledgtrst
    @Notsoskilledgtrst 14 років тому

    THANKYOU patrickJMT!!!! Your videos are far superior to my calculus lectures, Its great being able to pause and rewind them whenever I need to stop and think. THANKS

  • @GJediAR
    @GJediAR 11 років тому +1

    Some how there should be a Law for all Calc Professors and Teachers to watch you and learn to teach in that way, at least the ones that I had the unfortunate luck of having.
    Thank you very much Mr. JMT

  • @patrickjmt
    @patrickjmt  13 років тому +2

    @chengyman2009 well, yes, you can teach yourself this stuff (do not see why not), but it is also new to most people and a bit confusing so it can of course be hard to teach yourself.
    there is no way to do math other than to practice. also read the proofs and think about why the results are what they are. to me, there is a lot of rules, but they all make sense because i have not just memorized them but also have taken time to understand WHY they are that way.

  • @grantclark4139
    @grantclark4139 6 років тому

    Thank you! I've read this in a few places but seeing it demonstrated finally made it click in my head.

  • @chandy141
    @chandy141 15 років тому

    You need to get the word out about these videos. These are so much better than anything I have seen, including what my calc teacher, who teaches at a top prep school that will remain un-named, does on the board

  • @nyjets2020
    @nyjets2020 10 років тому

    its incredible how well you teach this. you have a talent

  • @chejooriberam3371
    @chejooriberam3371 5 років тому

    Hey Patrick! I dony usually comment on videos in youtube. I payed a lot of videos to understand these convergent stuff and finally, with your video I did understand. THANK YOU A LOT

  • @mikeroch2384
    @mikeroch2384 11 років тому

    I would just like to take the time out to thank you for all your help!! You are seriously amazing! Thanks for all your time and effort. You really have improved my calc grade dramatically! Just awesome :)

  • @mytwohands
    @mytwohands 12 років тому

    Thank you so much for these videos, Patrick. I got through Calc 1 (online!) with khanacademy, but he's really lacking in Calc 2. I ended up finding your videos instead. I have a feeling they are going to get me through the rest of the Calc series. All your sequence/series stuff has been so helpful.

  • @cathyphilip7315
    @cathyphilip7315 3 роки тому

    I truly appreciate all ur videos through out my study..you are a genius and life saver

  • @matchamutcha
    @matchamutcha 14 років тому

    I'm so glad u can explain it step by step clearly, unlike my teacher, who just told us the ratio test, radius of conv, interval of conv, and nth tearm test all in 50 minutes....i don't even know what i learned that day

  • @heresatissue
    @heresatissue 12 років тому

    Thank you for all the uploads!

  • @patrickjmt
    @patrickjmt  12 років тому

    @limetang no, i rarely do proofs since i figure they are already in the book! i have thought about doing some though

  • @stillfreeman2
    @stillfreeman2 11 років тому

    Hello Patrick. Your videos are great, it's just that you go through so much detail explaining everything you do. You could save a lot of time if you didn't. And if someone doesn't understand they'll repeat the video. You'll be able to solve a lot more examples in one video...

  • @P10strings
    @P10strings 11 років тому

    Patrick, thank you so so much for posting these videos and sharing your knowledge. My professor is maybe too smart to teach us "average Joes and Janes." You make it much easier to understand. Thank you for all your hard work. I'll probably later today buy your series handouts to get actual practice with easy to understand answers. Thanks again.

  • @danialissa4588
    @danialissa4588 6 років тому +1

    I have my cal II final tmrw... thank you for teaching me the topics of the last 5 weeks in less than 2 hours!

  • @Fruleo
    @Fruleo 12 років тому

    I really like your clear and concise notes! Keep it up!

  • @jadehowler16
    @jadehowler16 5 років тому

    Thank you so much for these videos. Actually using this to study for a test I’m about to do. And I have done so with more of your videos. I appreciate you!

    • @jakigang4068
      @jakigang4068 5 років тому

      Essie's you you you you you you you you you can

  • @josesammut9396
    @josesammut9396 4 роки тому

    I'll be finished with the exam in 12 hours. Thankyou for taking care of my light revision at the end. Don't feel like looking over my work another time.

  • @mohammedabid9666
    @mohammedabid9666 6 років тому

    thank you for doing this. Even though this video is a decade old its still helping people in the future. Your videos saved generations of college students. I wish i can repay you somehow

  • @babathehutt
    @babathehutt 14 років тому

    Thanks for the super clear explanation and handwriting!

  • @patrickjmt
    @patrickjmt  15 років тому

    tryin' my best to keep 'em coming!

  • @patrickjmt
    @patrickjmt  12 років тому +1

    hahaha, glad you like my explanations :) lots of sequence and series stuff - a lot of it is in a playlist if that helps (but not all of it)

  • @patrickjmt
    @patrickjmt  14 років тому

    @jay2yosi glad to help!

  • @janmola
    @janmola 11 років тому

    Your videos help so much - glad I found your site :)

  • @Petros11888
    @Petros11888 9 років тому +70

    i dont know here you live, but I will find you and I Will hug you and tell you that i love you because i think you saved my ass

    • @patrickjmt
      @patrickjmt  9 років тому +36

      austin tx. i love me some hugs.

    • @Petros11888
      @Petros11888 9 років тому +7

      exam is on Monday.Whatever i dont know ,you have a video for.If I pass Im flying over there to find you.

    • @Petros11888
      @Petros11888 9 років тому +4

      Bianca Arantes Oh right, I forgot to give an update.Yes I passed! 6/10

    • @pierrefabela
      @pierrefabela 9 років тому

      patrickJMT Road Trip!!!

    • @Petros11888
      @Petros11888 9 років тому +2

      Bianca Arantes so,how did it go?
      pierre fabela yea...i was kinda overexcited at that moment.I cant keep my promise :(

  • @axeknight4653
    @axeknight4653 4 роки тому

    Thank you! Nice, simple and straightforward explanation.

  • @6markiv
    @6markiv 13 років тому

    i live all the way in kenya and you are the best teacher ever. thankyou so much patrick

  • @castelinop
    @castelinop 13 років тому

    Hi, thnx a lot. I was stuck on this part of my calc course. Went through my textbook a couple of times but didnt really make sense. Your video cleared my doubts. Love all your videos.

  • @shycrypt
    @shycrypt 11 років тому

    Thank you so much for this. Just did this topic in Cal 2 and i didn't understand one shxt until i watched this. Got it in just a couple minutes. THANK YOU SO MUCH!!!!!!!!!!!!!

  • @JennieBMurphy09
    @JennieBMurphy09 8 років тому

    You are my savior if it wasn"t for you I would be lost and confused. Keep doing what you're doing but you are absolutely amazing at explaining in a clear way! I love you - not kidding!!

  • @henkpietjaaphein1122
    @henkpietjaaphein1122 14 років тому

    It's amazing that it's possible to learn these things by watching your videos only once!
    100 stars!

  • @AkshayBala__007
    @AkshayBala__007 6 років тому

    Great work, Patrick brooii!

  • @oakkles
    @oakkles 14 років тому

    you are amazing!!! I wish i had found you before i took my midterms, it would have helped tremendously! thank you!!!

  • @btran92
    @btran92 13 років тому

    god bless you :D your so helpful. When ever I cant seem to grasp the concepts i watch your videos and everything is cleared up. Keep the good work up! (your saving thousands of student from failing calc 2 hahaha)

  • @patrickjmt
    @patrickjmt  13 років тому

    @stevens0625 the video is called ' Strategy for Testing Series - Series Practice Problems '

  • @maingedang
    @maingedang 12 років тому

    Your videos are so helpful! I can't thank you enough.

  • @patrickjmt
    @patrickjmt  13 років тому

    @castelinop thanks, glad u like the vids

  • @mrinalpramod913
    @mrinalpramod913 6 років тому

    You are a lifesaver. Youve got everything!

  • @ranjuramesan4167
    @ranjuramesan4167 7 років тому

    i always count on u during my exams.. thanx a lot man.

  • @sherryge1520
    @sherryge1520 5 років тому

    I do think your interpretation of the theories of Mathematics is easy to understand. Thank you very much indeed!

  • @jennosyde709
    @jennosyde709 7 років тому +1

    You are a wonderful person. Thank you so much for this video.

  • @fttank
    @fttank 14 років тому

    I have my calc. exam tomorrow at 4, and let me tell you that you are saving me right now.
    KEEP IT UP!! =D

  • @ian559fresno
    @ian559fresno 12 років тому

    @patrickJMT Dude you are seriously the BEST! I dont know why the books make this soooo complicated. You are awesome! You should make your own math book!

  • @abdoxxg36
    @abdoxxg36 7 років тому

    thanks a lot . love your style in the explanation

  • @phebes2009
    @phebes2009 15 років тому

    I appreciate all your videos. These all all I need
    to pass my exam.
    (Sad to say but most textbooks confuses me)

  • @aromanous
    @aromanous 13 років тому

    Your a Gem! You should do a video on Integrating factor!

  • @wrinklywitwicky
    @wrinklywitwicky 13 років тому

    i don't know if you'll see this but you're a life SAVER DUDE. THANK YOU. the 7 odd minutes you spend takes my lecturer 2 hours to attempt doing, and no one understands a fuck he's saying

  • @hahahahaha9764
    @hahahahaha9764 5 років тому

    Kudos to you it really helps legit to think that things that I pretty much was having a hard time can be understood like this really thanks man.

  • @rowemania21
    @rowemania21 13 років тому

    you're teaching class at the University of South Carolina too..thanks for helping me pass, I wish i would've found your channel YEARS ago

  • @JORELY21
    @JORELY21 14 років тому

    thank you so much for doing this exercises ....you help me a lot to understand it

  • @patrickjmt
    @patrickjmt  16 років тому

    you would not to use the ratio test with rational functions (polynomial divided by a polynomial) as the ratio will always be 1, which gives an inconclusive result. some other technique must be used! typically, i try the limit comparison test in such situations.

  • @CosmicAnomaly313
    @CosmicAnomaly313 14 років тому

    Thank you very much?Really this is an excellent guide into the ratio test,excellent and thorough, thanks again,keep up the good work.

  • @steelbluesleepR
    @steelbluesleepR 13 років тому

    watching this the night before the test here at Missouri S&T, wish i'd found these videos earlier!

  • @Murderburrito
    @Murderburrito 15 років тому

    Thanks dude so much! u helped clarify things for me

  • @Ethiopianraver
    @Ethiopianraver 14 років тому

    thank you so much for these videos, your a life saver

  • @firstnamelastname3106
    @firstnamelastname3106 8 років тому

    thanks man, it's really useful!

  • @autobahn2501
    @autobahn2501 10 років тому

    Thank you. It's really helpful.

  • @patrickjmt
    @patrickjmt  15 років тому

    no problem!

  • @diyarkhalid
    @diyarkhalid 10 років тому +1

    Thanks for this explain

  • @albertech445
    @albertech445 3 роки тому

    Thank you sir, I don't know whether you see this but still the session was effective.

  • @abbeyeads9419
    @abbeyeads9419 3 роки тому

    Such a good explanation

  • @AKASHSARATH
    @AKASHSARATH 8 років тому +1

    You are my Math God. Thank you

  • @beutifulamit
    @beutifulamit 11 років тому

    I think the hard part about this is not screwing up the alg :3
    THANKS FOR POSTING THIS.
    i feel better about my test tomorrow :3

  • @stephenhuang382
    @stephenhuang382 6 років тому

    SO USEFUL!! THANK YOU :D

  • @patrickjmt
    @patrickjmt  14 років тому

    @gsowx2 i have a video somewhere where i go through about 20 series problems discussing what exactly i would be thinking about and what test i would use ( i do not actually solve any of them)

  • @AmberComer
    @AmberComer 12 років тому

    Thank you so much. You really help me so much! I know that, no matter how confused I am after class, you'll probably have a youtube video about it and I'll be okay. :)

  • @jenoharu
    @jenoharu 7 років тому

    i owe my math series to you. thank you very much!

  • @adamlebrun1615
    @adamlebrun1615 10 років тому

    The good old days of the 10 minute time limit. Great video!

  • @masterlight5
    @masterlight5 13 років тому

    wow thank you patrick i finally understand it now!

  • @harshittiwari9558
    @harshittiwari9558 5 років тому +1

    Thank u so much for explaning this

  • @mrthatguyification
    @mrthatguyification 12 років тому

    @vaticanantichrist you have (n+1)^2/(2^(n+1) * 2^n/n^2 , for the first denominator you can separate 2^(n+1) into 2^n * 2^1. so the 2^n that we just created and the 2^n on the second numerator cancel and you're left with the first numerator(n+1)^2/2^1 * 1/ second denominator ( n^2)

  • @patrickjmt
    @patrickjmt  15 років тому

    well... go forth and spread the word!! : )

  • @varungodavarthi2262
    @varungodavarthi2262 4 роки тому

    Good explanation sir !!

  • @romero4742
    @romero4742 12 років тому

    Great videos bro keep it up :)

  • @phalvin93
    @phalvin93 10 років тому +16

    Mr Patrick, what would I do without your videos?
    Kudos to you & keep making awesome videos like this :)

  • @fiorellavt1
    @fiorellavt1 15 років тому

    thanks
    you make math easy to understand.

  • @nishantsharma4826
    @nishantsharma4826 5 років тому

    A Huge thanks to u, you are better than my teacher

  • @bighorn2004
    @bighorn2004 15 років тому

    nice video, you really have a talent for teaching

  • @Gawkie
    @Gawkie 7 років тому

    hello Patrick, first of all thank you so much for these videos, theyre the only reason I understand calculus
    2nd, I have a question that I hope you can answer
    how do we test a limit that has a sine or cosine in it, like this one for example
    k+(cosk)^2/ 2k^2+k+7, from k=2 to infinity
    thank you in advance

  • @sarsuraaa
    @sarsuraaa 11 років тому

    why do u place an absolute value??
    you are awesome :D

  • @AA-ht3ce
    @AA-ht3ce 6 років тому

    people still learn from you in 2018!!! 10 fucking years THANK YOU!

  • @udaramaligathanna4882
    @udaramaligathanna4882 Рік тому +1

    thank you !👍

  • @gambit1357
    @gambit1357 14 років тому

    OMG i'm soo glad i found you!!!