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

[xxTH3EMPIRExx]

How do you no pass out from all the sharpie fumes? great vids btw

[SuperPointz]

DAM his sigmas look sick

[AasinApples]

@SuperPointz lol for some reason i just found it funny seeing a comment like that on calculus video.

[kenikozo]

I FUCKING LOVE YOU

[ian559fresno]

hahahaha this is the exact same problem in my book :D

[ian559fresno]

Why is this class so hard? Thanks for the videos.

[killerfox67]

hey patrick its jeff, i love ur vids and constantly find myself looking you up for math help, I am however having a difficult time understanding why at time 2:46 the 2^n and 2^n+1 simplify to a value of 2. I just dont see why the denominator loses the 2^n+1, a response would be greater appreciated! thanks

[Filmrdian]

@killerfox67 Basically when you have two to the n (some integer) and 2 to the n (some integer) plus one more, the 2 to the n parts cancel, leaving just the one more, one.

I'm not sure if that makes sense, but that's how I work it out in my head as I'm doing the problems.

[limetang]

Do you have any videos of a proof for the ratio test?

[patrickJMT]

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

[vaticanantichrist]

@patrickJMT Can you help me? In the video @ 2:40 you reduce the 2^2+1 to a 2 i cannot see how you possibly got that? If you reduce from the 2^n everything should go away. I am confused

[mrthatguyification]

@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)

[1878DJM]

Dude this was the first question on my exam today(n^2/2^n(... got full marks; I had seen it before on here lol is right(scouse for nice one)

Question for you, why was ten afraid of 9?

[umbragami]

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. :)

[nateahmed]

ur awesome

[BigDeck10]

would be failing calc without you

[megaripcord]

the only thing i watch more of online then your videos is porn. and thats alot

[1878DJM]

@megaripcord hahahaha

[mytwohands]

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.

[patrickJMT]

@mytwohands tons of calc stuff here ; ) 

[romero4742]

Great videos bro keep it up :)

[barnacleboy1000]

Hi,

Firstly I wanted to thank you for making this oh so clear!

Secondly, I just have one question: why did the (-3/4) in the second solution become a positive?

Thank you again!

Lisa

[AznVamp24]

@barnacleboy1000 it was in an absolute value when he changed it to have the limit. Ratio test is defined as lim n-> infinity, abs(an+1/an) = L

abs == absolute value.

[Mikenike2890]

I'm a little confused at one point in your video. At 5:31 you're simplifying and you include the 4 in the denominator. Can you explain why the 4s don't just cancel out? You say you have 4^n on the bottom, and then you say you have n-1 in the denominator. I'm guessing you meant numerator, but I'm still not sure why there is a 4 in the denominator after you simplified it. Your video is very easy to follow, this part just has me confused.

[Mikenike2890]

@Mikenike2890 Never mind. I understand what you did.

[alrasw]

I tag myself (alana) and you (patrick) in your drawing at the start of this video!!

Luv u!

[patrickJMT]

@alrasw hahahaahha!

[wrinklywitwicky]

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

[patrickJMT]

@wrinklywitwicky happy to help : )

[TheKingstoncowboy]

I dont get the cross multiplication at 2:40....

[splint3048]

@TheKingstoncowboy 2^n cancels with 2^(n+1) leaving 1+1=2 multiplied by n^2 in the denominator and in the numerator is (n+1)^2 expanded to a polynomial.

[paperfreeck]

I have a question: lets say we have a_(n+1) = (3n-1)/(2n+5)* a_n and a_1 = 1/3

I am confused about the role a_1 plays.

[paperfreeck]

@paperfreeck so if I solve I get 3/2>1 so wwe are dealing with divergence?

[dysfuntionalo01]

WOW! i go to class everyday and stare at my text book and it takes me forever to understand... thats if i understand at all. I watch your videos for 10 mins or less at a time and i understand it instantly. your videos are CHAMPION! too bad you dont do physics and chem or any of that. THANKS A MILLION!

[shebotnov]

and what would you if you had n^100, and not n^2. You'd that had (n+1)^100. What then?

[6markiv]

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

[KingLiamYNWA]

hey great vids really help!! i am jus wonderin if the series doesnt start at n=1, say it starts at n=3, when seeing if it is convergent or divergent do u still say if the answer is greater than one its convergent, or would it be if it was greater than 3 it would be convergent, since the series starts at n=3 and not n=1?. . .myt be a stupid question bt m not sure so i better ask jus in case :P anybody who knows feel free to answer!

[cvfox89]

Nerds Rule!!!

[beeg777]

great job sir

[btran92]

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)

[zok1i]

thank you so much, your videos helped a lot.

[masterlight5]

wow thank you patrick i finally understand it now!

[stevens0625]

I know this may be a elementary question.. but is it possible for a series to Converge using a certain test and Diverge using another? thanks!

[1ordofsarcasm]

THANK YOU SO MUCH!!!!!! You made the impossible stuff in my math book seem almost easy! Keep it up! This is so amazing!

[guitarhamster102]

dude you should teach at MIT or something because you're one of the most amazing teachers ever.

[13xxxbigboyxxx13]

i love this and Khan Academy, both awesome

[Davids2trill]

I am struggling with finding the sums of infinite series and using partial sums do you have any videos for that?

[pimpmymail]

You keep gaining my respect over and over again.

[chengyman2009]

Patrick, I am having a hard time remembering all these test for sequences and series....Our Test is Next Thursday is practice the best way to learn these test....Our teacher sucks, and i was wondering if it is possible to teach ourselves series and sequences??

[patrickJMT]

@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.

[ian559fresno]

@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!

[nicholasawrey]

Seriously amazing. Sat in my class for two weeks and didnt understand this stuff and you cleared it up in four minutes. AWESOME

[nogoodnamesleft111]

would this be an alternating series?

[nogoodnamesleft111]

i'm getting sick of sergio sanchez

[thechanel1986]

I'm a little confused as to how you simplified 2^n / 2^(n+1) to 2. Can you explain that please?

[RatherBeWatchingPorn]

@thechanel1986 If you look at the denominator 2^(n+1) you can think of this as 2^n * 2^1 simply by the rules of exponents of like bases (in a generalized form, x^a * x^b = x^(a+b) which makes sense due to the associative property of multiplication). So by extension, 2^n * 2^1 = 2^(n+1) and the reverse is also true. This is a common effect of the ratio test, and like he and most say, you learn math by doing :) This tripped me up at up first too, and I was wondering if any else did too... hah

[Aerlenbach]

You're left handed, and are awesome. Not a coincidence.

[mymojosodope13]

You are a true hero.

[fishfoodandfatcats]

does watching these videos instead of doing my coursework count as procrastination?

[steelbluesleepR]

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

[patrickJMT]

@steelbluesleepR spread the word! : )

[tokyo200]

Thank you. This is really helping me a lot. I hope you're doing okay.

Oh and greetings from Kansas. I am learning from you in a tornado on my farm. JK.

[TheTalmon18]

Patrick, how wouldi do this without using limits?

Im supposed to know whether or not a goemetric series is convergent or not, im in alg2/trig

And the books example does show a L --> infinity

Im so confused he never showed us how to do it=[

So im just ogna figure outlimits from this video now ;P

[lilyjune1230]

i really need help in terms of knowing how to simplify those terms. Do you know the general term for those problem sets? I want to google them for addition practice before i even work on the series test problems

[ironhead161]

Please come to Clemson!!!

[patrickJMT]

@ironhead161 clemson must come to me.

[ironhead161]

@patrickJMT *laughs* lol this videos are the only way for me to learn this stuff.

[RyuHanamichi]

Thanx a lot from holland!

[bichstewie]

i would have failed by calc c midterm if it weren't for you.

[zinadine92]

what if the limit equals 1, how do you do it?

great videos btw

[birdsofafeather1990]

@zinadine92 There are other methods. Look up Comparison Test, Root Test and Integral Test, for example.

[gagikRLHS]

thank you

[aromanous]

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

[birdsofafeather1990]

@aromanous There is one, i'm pretty sure. It's one of the things i have been struggling with and I've been making notes from it over Christmas, among other things.

[Mayreauangel]

I go to the University of the West Indies. My turkish lecturer doesnt speak English very well so I was really confused. Thanks so much!!

[katyak92]

I wish I found these videos sooner!! Not right before finals. They're so helpful!

[blacksuperman180]

NJIT loves you man

[rowemania21]

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

[smileisacharity]

Is there any easy way to determine which test to use, I wonder if you can make a video about that or if you a paper that you can scan it?

[I3urningi3laze]

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!

[Ayplus]

I've rarely seen limits done so beautiful. Much respect from McMaster University.

[mpatt79]

I've been spreading the word to others about you... you've been a huge help for me in my calc 2 class, thank you, thank you, thank you!

[mpatt79]

been spreading the word myself around my community college in PA, you do great work, thank you thank you thank you!

[AstarealRomance]

nice handwriting

[loganrs24]

Thanks alot man. I go to University of Texas. Very Helpful. I've been spreading the word about your work on youtube

[patrickJMT]

@loganrs24 go UT. i am off to the FAC in a few...

[Letsmakeamovie]

You are teaching my whole calc 2 class. We all talk about you here at SF State. Thanks for teaching the world!

[patrickJMT]

@Letsmakeamovie howdy SF State!

[Ayplus]

@Letsmakeamovie . He's teaching us calc 1. Lol dont ask why we're doing this in calc 1, cuz im wondering the same thing. . . .

[FaiththeHairstylist]

I've been watching your series videos all morning. I guess it's time for me to donate more money :)

[patrickJMT]

@FaiththeHairstylist ha!

[oliver18754]

And is this for college? Please this is urgent, please give me a reply to all of my questions as soon as possible. Thanks in advance.

[YourSoDom]

dude your a life saver, SUBSCRIBING :D

[Qk34life]

I wonder if you have a video explaining what do with factorials in a series. My professor says to use the ratio test for it or something among those lines, but i just don't know.

[TheNdya]

can you tell me how to know which test to use? either to use root test or ratio test? hmm. I'm confused.

[Tentenlaw]

@TheNdya : The root test is normally used if the function is being raised to the n power. Taking the function to the (1/n) power cancels those to the n power. Not useful if you end up with infinity to the zero power though.

Unless the above condition apply, normally the ratio test is used. :-)

[castelinop]

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.

[patrickJMT]

@castelinop thanks, glad u like the vids

[gsowx2]

I have a test soon over series, and not sure the teacher is going to tell us which test to use to see if a series converges or diverges, so can you explain what to look for when presented a series problem on which test to use? Are you looking for certain factors, or is it a trial and error kind of thing? For instance, we've learned, ratio test, root test, integral test, comparison test, limit comparison test, nth term test, etc. Its so confusing as to which one to use? Great vid too! Thanks

[patrickJMT]

@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)

[stevens0625]

@patrickJMT hey i was wondering the same thing! i can never decide how to approach a problem or what test to use. I tried to find the video but could not locate it. If you could tell me the title and give me a link that would be great! thanks a ton.

[patrickJMT]

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

[patrickJMT]

@i8urk1d9592 i used to teach, but decided i do not like standing at a board and lecturing. now i teach via the internets

[fizzmaverick]

dude i love you man...i owe you my engineering degree!

[JORELY21]

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

[amazingness818]

awesome, awesome, awesome!!!! thank you times 100! 

[Cruth8987]

the ratio test is brilliant

[patrickJMT]

@Cruth8987 it is good stuff

[trentcreek]

at least on these few he has been writing on paper. He can;t go back and erase things so I can keep looking back to what he wrote so I can follow better. On those white boards he likes to write stuff then explain in .002 seconds then erases it and already have something else already wrote down. Then I am like "what? what? what was that?"

[patrickJMT]

@trentcreek pause, rewind. very easy

[trentcreek]

@patrickJMT true, true.

However I would prefer to have them side-by-side to do a comparison of what was done to make sure I know what is going on.

JMT: Just Mean Tester ;-)

[patrickJMT]

@trentcreek so open two web browsers : )

[ChasingMalavika]

You have a sexy voice! And you're doing math...A+ ;)

[patrickJMT]

@ChasingMalavika ha, some say sexy, some say very annoying : )

[allghost1234]

There's only one thing that I don't like about Patrick: He leaves me no choice but to make me log into youtube just to say thank you because his videos or so damn GoOd!!! THANK YOU SO MUCH!!! You made me waste 1 minute of my time but helped me save 12957129041283021 hours spent in my boring class..

[patrickJMT]

@allghost1234 hahha, i will start making my videos really confusing with tons of mistakes from now on out : ) that way you will not be tempted to waste those precious minutes!

[majidnaeimi1360]

Hey Man...You are doing exactly great...thanks a million....I have a question concerning series and sequences...I have seen in some books about boundedness and convergence of both series and sequences...what is the different between them? can a series be bounded? or do we have a convergent sequence? how are these terms different or related.(Series, sequence, boundedness and convergence)...

[babathehutt]

Thanks for the super clear explanation and handwriting!

[T3nnisstud510]

You are a grade saver. which makes you a life saver as well.

[gaintteam]

thank you very much

very gooood

[PlayTheCold]

u rock thanks

[2PACmosDEF]

Thanks a lot for this video! its great, its the one thing that's enabling me to pass calc, haha.

[jay2yosi]

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.

[patrickJMT]

@jay2yosi glad to help!

[EmperorCesar]

patrickJMT, you are one stone cold n***er.

[1aaronaaron1]

you have some wicked looking sum symbols

[coolkid19901]

This is for Geometric right because it involves a ratio

[oakkles]

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

[gambit1357]

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

[kerryvp]

dude!! u rock so hard

[kchou0202]

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

[zskarimi]

Wow!! you are just amazing! You helped me alot, tnx. pls keep on sending!

[borisvankatwijk]

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

100 stars!

[patrickJMT]

glad you did not have to come back a second time to be bored by me!

[kimpoi00]

if the ratio test is 1.. the test fails! absolutely correct!! i got 1 over 100 in my test and it fails!! whooh!! unbelievable!!

[fttank]

I have my calc. exam tomorrow at 4, and let me tell you that you are saving me right now.

KEEP IT UP!! =D

[sannykh]

god bless you man...you helped me big time.

[Notsoskilledgtrst]

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

[bornlegendz8]

thank you so much!!!

[harry736894]

Dude im gonna use u for my exams this term!!!!

[alexPsanz]

HEY thanks so much. really appreciate it.. i know u hear this all the time but w.e man, thank u!

[tsd5060]

i dont understand why the 2^n+1 cancelled into 2...shouldnt it cancel into 2^n?

[ibethgc]

dont forget that 2^(n+1) = 2^n*2^1

the 2^n on the top cancels out with the 2^n on the bottom leaving you with 2^1 bottom

if that's what u asked 4.. hope it helps.

[gruntparty]

when you split up 2^(n+1) its equivalent to 2^n + 2^1, thus the 2^n 's cancel and you're left with 2

[edhernan534]

dude, i also thougth it wa 2^n ... but he is right its (1/2) ... to prove try substituding any number to n and u would end up with (1/2)

[sn00pking]

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

[Avi0107]

thanks! very helpful

[Vipergunman426]

dude, i have a test friday in calc 2 and im watching your videos again. they help way more than the book does. and you actually do true examples, not just some easy thing to show a proof. keep up the good work and thank you.

[Ethiopianraver]

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

[nhl3002]

hi!, does it change anything if our series goes from, let's say, n=4 to oo  instead of n=1 to oo ?? Thank you, great videos by the way!

[lefty1042]

thank you, thank you, thank you, thank you!

[BlessureK]

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

[olip99]

Thanks so much! very helpful!

[WammyHammy]

When looking at a problem, how do you determine which test to use of all of them. Such as the ratio test, alternating series, p series, etc.

[OutrageousElephant]

how do you know when to use the ratio test?

[patrickJMT]

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!

[OutrageousElephant]

thanks!

[30x60]

is the process the same if the given is for example:

(x^k)/k!

[Nanumir]

another amazing video by Patrick

[wkiafu]

Patrick,

Is it true that when we are doing to limits, we are putting them as an absolute value? And so when we take the constant out, it will always be positive?

[wkiafu]

or can you explain about why are you putting absolute when we are doing the limits?

thanks.

[QbanoPuraSepa]

You saved my A+ for Cal II, you rule!!!!!!!!!!!

[walkonwalls]

way better then my 'math for engineering' lecturer. dude u rock!

[urtocool26]

YOu saved my Life!!!!! I have a midterm at 8am! Where do you teach... if you ever move to california cal poly pomona would love to have you! All the future engineers could use some better math teachers!

[younesb91]

Good !

[gerrenx7]

may the Gods Of Math Bless you

[phebes2009]

I appreciate all your videos. These all all I need

to pass my exam.

(Sad to say but most textbooks confuses me)

[bighorn2004]

nice video, you really have a talent for teaching

[RadoAller]

u think???