Geometric Series and the Test for Divergence - Part 1

[Carebearbull]

Why so series Patrick?

[tijuanamarisol666]

4:44 it simplifies to 6+2/3

[anakmudajaman]

I Love The Video Geometric Series and the Test for Divergence - This video has follow up examples It Can Increase My Knowledge

[AntoMelta]

Good, I like that you share this video Geometric Series and the Test for Divergence This video has follow up examples, I wish success always

[willamricard]

Nice Video Geometric Series and the Test for Divergence This video has follow up examples That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video Geometric Series and the Test for Divergences This video has follow up examples! From Your

[bundawartini]

Your Video Geometric Series and the Test for Divergence - This video has follow up examples Is Very Useful Sharing

[gmdsl]

god! thank you very much. i just learned more about series in your videos than i have from all semester

[296967]

thank you im saudi and i understand from you better than my teacher

[michaelclark195]

Patrick - your videos are amazing. I can't even begin to thank you enough. You are the secret to calc BC

[LocalStrongMan]

dont worry patrick, the dislikes are only by people who failed calc then found these vidoes

[russ4553]

Patrick, if I may be so bold as to be on a first name basis, I just wanted to take a moment out of my day to thank you because you've taken so much time out of yours to help me. As I type this I am also lighting the candles to your shrine as well as clearing away the countless gifts that lay before it other patrons have contributed. Stay well hombre.

[supaheroman]

that divergence trick just blew my mind!

[Denixdaplayer]

Patrick, I have one little doubt about these Geometric Sequences. In your example that involved (pi^n)/(3^(n+2)); don't we have to leave it exactly like the Geometric Formula a(r)^(n-1)? Because it will involve further steps ratter that those you just did :S

[Josh1billion]

PatrickJMT's stuff on Nixty is very useful. Do as he said and go there and search for sequences and series.

[LocalStrongMan]

7:25 did you draw that penis on purpose? love the vids man, three years of calculus and ive learned more in 2 hours watching you work magic, keep it going

[sandau44]

This is awesome, you have saved my life. Thank you so much.

[animekitty0]

You are amazing!! I was lost, but now I know exactly what to do. I feel like crying I'm so happy.

[djsneaks2]

teacher goes over proffs, while you teach me how  to use the formula.

thanks =]

[TheChaima21]

I'm in love with you man :D

[McBirdec]

i spent an hour looking for this using google.  i should've came to PatrickJMT first

[patrickJMT]

@McBirdec now you know : ) tons of sequence and series stuff on here!

[patrickJMT]

@McBirdec i also have free quiz / test materials on nixty with solutions to the problems if you are interested

[R0kmyS0X]

@patrickJMT what is nixty please, I would really appreciate some free quizes

[patrickJMT]

@R0kmyS0X just a web site, check it out and do a search of ' sequences and series ' in the course list.

[R0kmyS0X]

@patrickJMT Oh haha thanks. Got a math final coming up :p

[ian559fresno]

@patrickJMT Free quizes?!?!?! you are the BEST!!!!!

[blaky112233]

Thank you soooooooo much for this videos! i was soo lost during lectures but now i can see the light!! ...i can hear the halleluiah chorus! lol THANKS!!

[starlight200816]

Thank you thank you soooooooo much for these videos. I felt so lost in my calculus 2 class today its not even funny. Your so much more clear than my professor!!!!

[lIJakeIl]

No joke, I just learned more about infinite series form this ten-minute video than I have from attending lecture all semester. Thanks man.

[patrickJMT]

@lIJakeIl no problem, tons of sequence and series videos on here by me!

[R0kmyS0X]

PAT guy who pulls a bag full of tricks out of his HAT, knows math so well, he could probably teach his CAT. YEE

[zarfanhussain]

may God bless u patrick and guide us all..

[dannyoideth]

@patrickJMT . I am Mexican and I try to see these lessons in my language (spanish). But I didnt understood any of them. Fortunately I found your videos, and I understand most of them. I really appreciate your videos, thank you very much patrick. (Forgive my bad english)

[BangingBox]

PatrickJMT, I LOVE YOU lol no homo!!!!

[dazebhen1]

is patrick from australia ?

[tastysauce]

Despite being a senior comp sci student at UC Davis, I don't know math, and you are definitely saving me 1 video at a time. I noticed you said we could donate. How do I donate?  I wish I could just give my summer quarter tuition to you ;P

[Buhagru]

I am a 16 year old student studying pure Maths Advanced level in Malta and I truly appreciate your videos! I always find some difficulty understanding stuff in Maths but your method of explaining makes things much more simple to understand. so thanks a really lot!

[thaonhi19tth]

i got an A in pre-calculus..thanks for your tutoring..:)

[gollek12]

Thanks so much. You got me an A+ in Algebra II. You make math so much easier than my teacher does. You are awesome.

[unarmed1234]

fuck the green hornet i wanna watch the video

[apex28del]

Thank you so much for all your effort. Something tells me that me and at least 90,079 others owe you a beer (or your beverage of choice)! If it was up to me, YOU could have my tuition money....

[chengyman2009]

HELP!!! TRUE OF FALSE: ALL GEOMETRIC SERIES CONVERGE?????!?!?

[gMEEE]

@chengyman2009 false. i suggest you watch all videos on series.

[chengyman2009]

For problem 3, if r was between negative. 1 and 1. And you went on to fight what the series converges to, will you multiple by the number that you pulled out in the beginning to make a geometric series? Thanks Patrick.

[MikeyIV]

Hi,

In the problem at 8:00, that is not a geometric series (right)? So for geometric series you use R to determine whether it is convergent or divergent, but for ANY OTHER SERIES TYPE, you can use the divergence test, am I right? I have an exam tomorrow, so please get back to me as soon as possible.

THANKS AGAIN

[mamatela]

THANKS FOR EVERYTHING, BUT WORD OF ADVISE...... YOU SHOULD PROBABLY GET A SMALL WHITE BOARD THAT WAY YOU WON'T HAVE TO USE THAT MUCH PAPER.....SAVE TREES! :)

[patrickJMT]

@voidwareprohibited yes, i know people are very appreciative! that is why i keep making the videos. i wish all i had to do is sit around and make videos.... i'd be happy, people out there would be happy : )

[jayspenh]

How come you do not have Harmonic Series on your website?

[patrickJMT]

@jayspenh cause it is impossible to make videos about every singe thing that everyone wants to see. if everyone started making donations (never ever going to happen), i would sit around and make videos all day. until that happens, i work and do this in my spare time.

[jayspenh]

@patrickJMT okay that's fine. i would donate if i had a job i think you deserve it. i understand you and not the professor. if you ever get a chance can you do harmonic series please?

[Ak120691]

@patrickJMT thanks for the vids Patrick. You helped me to hopefully pass my calc class. I got a 48 on my first and the class isn't curved. I managed to pull a 70 on the 2nd midterm and hopefully I'll do semi well on the final.

Convergence tests are a killer for me though.

[KillerZero259]

@patrickJMT why wont you allow for donations? 

[patrickJMT]

@KillerZero259 i do allow for donations on my website. feel free to go make one :)

[mzellars822]

You da man

[soso2282]

you're the best

[jiamonx2]

i noticed that i don't fall asleep to your videos, and when im in class i always fall asleep

[koreankid28]

Unlike many other people, I do have an amazing Calculus teacher, but I hardly have the time to get tutored from him after school. Reason I get tutored by him is because I'm in Calculus AB because I couldn't fit Calc BC into my schedule. I've been a bit behind on things than the Calc BC students, and now I found your video and I finally understand this convergence and divergence stuff. Thank you!! Now I have hope for doing well on the Ap exam.

[dajakesta1234]

so u dont do anything when u test it out and its diverged?

[mebonite123]

I MUST SAY...i am a bio-chem student. i go to a university, and i am pretty much a math minor just because of all the math i have to take for my major. Honestly patrick, you are amazing. words cannot describe how much you have helped me out. When i found you for calc 1. You SAVED my life. FOR REAL. honestly i dunno what i would do if it were not for you and your free vids. THANK YOU

[bamagirlqtlicious]

Ok. So I've been watchin all these videos and I'm not sure where I've missed it at but I understand how to test for divergence. So when you do the test and it's convergent it can still be divergent right? So how do you determine then if it's actually convergent or divergent?

[TheWolfBlitzer]

u got urself a new subscriber, im self teaching myself with the help of your videos through calculus, its hard but i will never quit, i will finish what i started. :D

[Umi2424]

Great videos!

You should get a whiteboard though so you don't waste so much paper. (:

[nowknow0123]

@Umi2424 he uses one in his newer videos lol

[tokyo200]

I learn alot more from you than my teacher.

My teacher just goes really fast on this subject. ( so many tests for convergence and stuff )

I know this should be easy stuff.

Does this make me dumb?

[Umi2424]

@tokyo200 This should be easy stuff? My teacher has been telling everyone throughout the entire year that Sequences and Series are the hardest part of Calculus, haha. I really hope this isn't supposed to be easy! (:

[doubleja]

General form of summing the geometric series a(r^k) from k to infinity is:

a(r^k) / (1-r). Thank you for pointing out what my calc 2 textbook fails to do.

[asusminor]

Quick question does the little formula that is in the video response work, or is it just a consequence of the selected numbers???

[Umi2424]

WILL YOU MARRY ME?? I LOVE YOU SO MUCH!! I might actually pass my AP Calculus test because of you....

[lizziedoll456]

The 9 people that dislike this are at liberal arts colleges.

[patrickJMT]

@lizziedoll456 if i were a prof, i would much rather teach at a liberal arts college

[td904587]

@patrickJMT why?

[sarmstrong6431]

@patrickJMT and yet you have manly republican commercials curious...



[patrickJMT]

@sarmstrong6431 i hope this is a joke

[07jenrose]

Don't you have to divide -1 IN THE SECOND TO LAST EXAMPLE BY N^2?

[dajakesta1234]

never knew einstein had a son XD

[bloodhoney360]

@dajakesta1234 Einstein's dont breed - they clone

[mariomaruf]

"Geometric Series and the Test for Divergence" sounds like a Saturday morning cartoon "series" except you replace "Test" with "Quest."

[Rhonnie2094]

I announced to my Calc.3 class today that there was a saviour online :P

[smilerLFC]

Nice one patrick. Doing this all for free!!! One day it will pay off for you. I can't learn off 'ANY' teacher..... but you i understand.

Most tutors are lazy but you explain everything.

Im currently at University and don't understand them what so ever. It really got me down and thinking i can't do this but you gave me hope. My tuition fees should go to you. Instead they increase them.

I don't think you realise how good you are.

[patrickJMT]

@smilerLFC glad you like the vids : )

[lxoxl]

@smilerLFC welll..we have to watch the ads so hes making money off this

[JameSunday]

Hey Pat, I just wanted to know I love you and your videos! They have helped me soo much =) Also, do you have partnership w/ YouTube? Because if not, I definitely think you should!

[ohgoodlord]

ALRIGHT, SO, IN THIS VIDEO

[patrickJMT]

@ohgoodlord sounds like me

[Spdowind]

you are like superman for math classes. 

[janvaguilar]

oh, follow up to my post, n=2

[janvaguilar]

awesome videos man! these really help.

just one question:

how do we know whether to use the divergence test (taking the limit as it approaches infinity) or the geometric series test (first term / [1 - common ratio])

i came across a problem where there seems to be no common ratio ( 2 / [{n^2} - 1] )

[paleeoguy]

Which video comes before this, sequentially? I cannot find a basic "geometric series" intro that leads into this vid... Thanks!

[mppotion]

How come you've never used a white board instead of paper?

Asides from that thank you so much for all your help!

[DuffxCrew]

I want to have your babies... no homo

[ShivMan007]

i love you.

[jay291]

Is there a practical use for these tests in the real world?

[patrickJMT]

@jay291 yes, for sure.

for example, when you take medicine and some residual drug remains, you can calculate the max amount of the drug that will ever be in your body using geometric series (so that you do not overdose)

[MrTitusRbandoline]

@patrickJMT Useful.

[tucker2056]

You're much more coherent than my professor, thank you so much. You're a great help!

[wittyocean]

hi. i got confused at the end of the video, the last example you got a limit of 1/2 and you said it diverges but i thought if limit exists then it converges and if no limit exists it diverges. just like you did for other problems..

[tucker2056]

@wittyocean The test for divergence regarding limits is slightly different. If the limit does not equal zero, then the series diverges. Don't get this confused with the integral test in which you also use a limit combined with an improper integral. In a case like that, if the limit exists, the original series converges as well.

I hope this helps.

[ezekiell666]

I bow down to you my lord

[masterlight5]

lol im going to 10th grade and taking ap calc ab. my teacher is sponsoring me for bc so i take the ap bc exam at the end of year. this vid helped me

[julieangel09]

How is it that I sit throw hours of class and understand nothing yet watch your videos and everything makes sense!

[abyification]

I <3 you.

[boatppy]

your video is very helpful.

[tattedupbiotch]

you are so freaking smart for doing these videos....they are helping me thro Cal 2! thanks!

[Dvoracekmara]

this are the same things

[SeanRVCA]

Patrick you're the man!

[KiwiLTK]

night before finals, thank u for always being there!

[jahnavimdave]

how to find geometric means???? can you please help me with this??

[Oviee08]

great videos man

my cal teacher may have 2 pHd's but he still can't teach half as well as you can

keep making more!!

[TwoMuchWork]

I love the videos dude! I don't want to sound nitpicky, but your left hand is always getting in the way of viewing the equation when you're solving. There's probably not a way to overcome that, but I usually pause just to read it.

[mrfish1991]

thank you sir!

I got more out of this 10 min vid than i did from 3, 50 min lectures

[hgybear]

What if it's 4 - 4/3 + 4/9 - 4/27....

[pgray10]

For a lefty you have neat handwriting

[kkk3006]

I like the way you teach... My Calculus 3 lecturer is making it hard for us.,,, I'll tell her to check out your Video.... :D

Thanks Alot!!

[jesusisstalkingyou]

god you make series more manageable, there's just so many converge/diverge tests i don't know which one to use.

[additionse]

thanks! you are very helpful...

[thien1234]

you're awesome , thanks so much :)

[janitarjanitar]

7:23 penis

[shasanni]

@janitarjanitar stay focused dude lol

[LukaLedoux]

If you do the test for divergence, and you find that the limit = 0, and you therefore do not know whether it converges or not, where do you go from there? For example, the limit 1/n is equal to 0, but how do you show that it is not summable?

[charlesc300]

you should be my teacher instead of the teacher that i have she is from ukrania and if i barely understand calculus in english imagine calculus in ukringlish

[thebestgameisrs]

wow your videos are very good

[METALsyndr0me]

danke dir!!!

[eckisfly]

i love youuuuuuuu

[jjjjanussessess]

thank you for this

[Ultimaxkeyblade]

YOU ARE MY LIFE SAVER

[beachplumm]

omg I want to marry you!! you are the best!!!

[sperckensiedoitch]

Thank you! THANK YOU!

[guitarsniper1]

you made my home work!!!!!!!your really cool you my teacher will give me extra credits for this im failing math....i hate my teacher cause were like in 2nd year high school but she's teaching us college stuff to hard....hey teacher!!!!! why dont you teach on someone your own size

[wtfamion]

TY a lot!!!!!!!!!!!!!!!. I nearly went shitape over my homework, i wanna shake your hands in real life

[erratic907]

you leave my professors in the DUST! thank you so much...i think i'm falling in love with you...

[sw33tbay]

u know.. my teacher doesn't even give that much information.. i F--*in hate when teacher does it like that.. they think their questions r hard enough n doesn't give enough info. anyway.. u r the best teacher ever.. I gona make A the class cuz of u.. thnx u thnx u..

[mygummies1]

LOL i go to your profile randomly thinking its my friend and i see you shuffling XD lol youre cool <3

[carvy922]

no me sirvio pa ni mierda!!!!

[nikesportman]

dude you're amazing

[mahlerite]

Good work, patrickJMT.

One can use the geometric series test for convergence to solve some probability problems, too. For instance, if we want to know the probability of getting a "heads" after EXACTLY n flips of a fair coin, it is P = (1/2)^n, as the flips are independent. We know that this series must converge to some number because -1 < (1/2) < 1. Thus, it converges to (1/2)/(1 - 1/2) = 1, or 100%. This tells us that, in principle, one must eventually get a "heads."

Personal marker: 3:32

[ellisar23]

you are the reason for my A in calc 2.. you're far better than any math teacher i've ever had.. thank you very much

[revangal3]

Totally agreed. I cannot understand my calc teacher... I have a D+ rite now lol. Just 2 quizzes and a test. I hope these vids can bring it up to a C or B.

[cchapar]

I will second that comment. 98 on my mid-term...my professor is decent, but its hard to understand through his accent. But u can never go wrong with Patrick.

Thanks so much.

[seththeseth]

i have a math teacher from China. just imagine the accent!

[bryanj12341]

thanks

[HomeDuDe123]

its nice listen to math from a teacher without a thick russian accent... this semester i have 3 russian teachers :S

[coolbluegatorade6225]

uic?

[ashek02]

Patrick,

the series a_n = n*n / (2*n*n - 1) diverges but the sequence {a_n} coverges to 0.5. Right?

[bryandPR]

i was wondering the exact same thing. but yeah i think you are right

[kartuned]

i thought it should of converge to .5 too. patrick, please help explain why it doesnt converge to .5.

thanks

[ohshedang91]

It's a divergence test, where it states "if the limit does not go to 0 then it diverges." Since it is not going into 0, it diverges.

[Nanumir]

so you do all this for free?

[Bloodvoid2]

Thank you so much for putting this up! ...I was planning on failing my test this afternoon in cal 2 until i saw this i really get it as a whole now thanks ALOT!!!

[Nanumir]

I know what you mean, I wish I had this resource back when I took Calc II

[cesfigas]

Thanx again, very helpful: greetings from Portugal....

[RogerTiger]

greetings from portugal squared! :D

[natzo89]

I have a doubt. In a text we use in my class, it says that to solve the series its something along the lines of

limit m->inf (1-r^m)/(1-r) = 1/(1-r)

Yet you use (first term)/(1-r), it's the book wrong or am I missing something?

[utheather]

Your book example is when m=1 (same as n=1 in this video and many books) for the summation starting index. The equation in this video is more general.

[CANADApei]

Thanks so much Patrick! I understand it now!

[wallacemckart]

man god bless u:)

[hectorlf]

dude, I just got a B+ on my calc 2 class just by watching your videos (and of course practicing on my own). I went to like 30% of my calc 2 class and still got that grade. I'm spreading the word man.

[patrickJMT]

go to class : )

and i am glad that the vids helped!!! : )

[doubleja]

@hectorlf

Writing my calc 2 midterm today in 13 hours. These videos are of tremendous help, especially since I've gone to less than 5% of my classes. The textbook is alright, but fails to be concise.

[k2ngofchaos]

i wish i discovered these earlier, ap test is tomorrow lol

[devin179]

haha yea me too

[ajantred]

man, you make this seem so much easier, my maths teacher is so boring i didnt get this until i found your vids. Keep it up :)

[Thel33t]

Those are some interesting sigma Signs :P

[yopoo123]

this guys has to be nominated for a "cnn Hero award". you're a hero man.

[patrickJMT]

hahahaha thats right! nominate me!!

[gerrenx7]

He Has My Vote for damn sure