WHY DID I BOTHER GOING TO CLASS FOR AN HOUR WHEN I COULD'VE JUST WATCHED 15 MINS OF YOUR VIDEOS AND UNDERSTOOD EVERYTHING MORE THAN EVER?!?!? YOU'RE SRSLY THE BEST
@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 : )
I'm taking the BC exam without a class and with as much help as I can get with a busy AB teacher so I've turned to test prep books, khan academy, other online resources such as yours. Thanks so much! I hope I can pass it on my own.
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.
You are seriously such a life saver. Before watching your videos, I was positive I'd fail my calc 2 exam. After, it all seems really simple and easy. Where can i make a donation? I can't offer much as a broke college kid, but you deserve my money more than any teacher at my university.
dude, you are awesome. my calc 2 teacher is completely awful and i understand it so much better when i watch your videos! thanks so much for doing this!
ok, if the limit equals 0, the series may OR may not converge, so that is not enough. the series given is an example of a 'telescoping series'; you may want to see my video on it : ) it is not a geometric series unfortunately
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.
I am a huge fan of your videos! I wish I could sufficiently show you how much your videos have helped me in calc 2, and now while starting calc 3. Don't know what I would have done without them. Thanks!
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
@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)
@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.
PatrickJMT, You will never understand how much I love you!!!! I don't care how good you are with numbers. There is no formula for this kind of love!! P.S. I'm destroying calculus because of you!
what can i say. u just so great. every time i stock. i come to search u ! you are my star. u made me want to be a teacher to help people .(even though, i don't think i can) :D . just love math.
At most universities or colleges, series occurs in your second semester, (Calc 2.) Diff EQ is traditionally meant to be taken after calc 3. However due to the gross similarities in the topics, such as trig, hyperbolic, and series, it is sometimes recommended to take Diff EQ right after calc 2. I have had several professors suggest this to me.
Always feels reassuring watching your videos. I was wondering what would drive you to make all these videos, but then again I see how many views per video you get, so no wonder : ).
when i first started making them, there was no monetization at all (for the first few years) i simply did it to help people cause i felt that is the right thing to do. i still make videos for that reason, getting a paycheck is an added bonus.
@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.
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!!!
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!!!!
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
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.
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!!
@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.
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
I believe that the n=3 is 10/9= 1.1111 not 20/9 = 2.2222. I did it along with the video. I don't know if anyone caught that. I entered it many times in my calculator and got 10/9. Great video btw! Helps so much
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?
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?
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
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....
Patrick! I had this silly test today ( at least it looked like so) one of the series asked to solve was: the serie from 1 to infinite of [ (1)/ ( (n+1)(n+2) ) ] I took the limit and I had it converges to 0... It's that OK? I mean, cos I could not see it as a geometric serie, cos i could not figure the R number... Ill be waiting for your answer... jesus im nervous
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.
nobody:
Annoying ad: "Are the videos from 2008 really helping!!!??"
me: Yes, they are really helping
Hey buddy, just wanted to thank you! This video is over five years old, but still helping people out!
+Afraz Jaleel Almost over 7 now... and still helping! :D
Ferris Bueller nearly nine years now 😂
Maddie O'Keeffe Damn lmao
I don't even remember what class that was from.. Calc 1?
Ferris Bueller I don't know, I'm watching it to understand a leaving cert question ( Irish exam)
Oooh alrighty
Good luck! :)
Patrick, you are freakin' awesome! You just explained to me in ONE video what an entire section of my textbook couldn't! Thank you so much!!!
Patrick, your summation notation looks like it belongs on the cover of a metal album.
you are amazing ShrindenZero
you are amazing Anna Lu
@@neethy1836 you are amazing neethy
you are amazing Evy Shen
@@mryup6100 You're breathtaking!
8 years and still helps ❤️
Nearly 10 years now and it still helps :D
@@quanganhvu4231 11 years and still helps
@@sashgnarg1498 12 years and still helps
@@assaultszn3557 14 years and still helps
Thanks, summer class is killer. Literally had no idea what my professor what was talking about when we started series.
I'm in that shoe right now
Manny M. That’s where I’m at right now. Watching 10 year old videos helps a lot more than lecture haha
WHY DID I BOTHER GOING TO CLASS FOR AN HOUR WHEN I COULD'VE JUST WATCHED 15 MINS OF YOUR VIDEOS AND UNDERSTOOD EVERYTHING MORE THAN EVER?!?!? YOU'RE SRSLY THE BEST
@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 : )
I'm taking the BC exam without a class and with as much help as I can get with a busy AB teacher so I've turned to test prep books, khan academy, other online resources such as yours. Thanks so much!
I hope I can pass it on my own.
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.
These are sometimes called GeoMadTrick Series because it's pretty crazy that an infinite sum can converge to a finite number (provided -1
You are seriously such a life saver. Before watching your videos, I was positive I'd fail my calc 2 exam. After, it all seems really simple and easy. Where can i make a donation? I can't offer much as a broke college kid, but you deserve my money more than any teacher at my university.
dude, you are awesome. my calc 2 teacher is completely awful and i understand it so much better when i watch your videos! thanks so much for doing this!
go to class : )
and i am glad that the vids helped!!! : )
Thank you so much for your videos! You're a great teacher. I was panicked about my Calculus II test tomorrow and you are putting me at ease. Thanks!
No joke, I just learned more about infinite series form this ten-minute video than I have from attending lecture all semester. Thanks man.
ok, if the limit equals 0, the series may OR may not converge, so that is not enough.
the series given is an example of a 'telescoping series'; you may want to see my video on it : )
it is not a geometric series unfortunately
@McBirdec now you know : ) tons of sequence and series stuff on here!
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.
I am a huge fan of your videos! I wish I could sufficiently show you how much your videos have helped me in calc 2, and now while starting calc 3. Don't know what I would have done without them. Thanks!
Calc 2 Test in 10 mins. Hoping for the best. Thank you Patrick for these amazing videos
Thanks Patrick! 11 years and still helpful :-D
You are amazing!! I was lost, but now I know exactly what to do. I feel like crying I'm so happy.
Thanks so much. You got me an A+ in Algebra II. You make math so much easier than my teacher does. You are awesome.
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
Thanks for using pen and paper and not paint! I didn't understand how to go about these problems at all before this video. Great job!
You make way more sense than my professor and the book. THANKS A LOT FOR THIS TUTORIAL!
@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)
@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.
Patrick - your videos are amazing. I can't even begin to thank you enough. You are the secret to calc BC
@lIJakeIl no problem, tons of sequence and series videos on here by me!
One of the most useful parts of TH-cam!
best tutor in my life
@patrickJMT Free quizes?!?!?! you are the BEST!!!!!
PatrickJMT,
You will never understand how much I love you!!!! I don't care how good you are with numbers. There is no formula for this kind of love!!
P.S. I'm destroying calculus because of you!
glad that you are crushing calculus :) keep up the good work!
what can i say. u just so great. every time i stock. i come to search u ! you are my star. u made me want to be a teacher to help people .(even though, i don't think i can) :D . just love math.
Honestly u are the best ever. i have been lost but thanks to u i am getting back on track... thanks u are awesome
13 year old video and still perfectly relevant.
god! thank you very much. i just learned more about series in your videos than i have from all semester
glad to help! when i post new videos, i jump around about topics! hopefully some of them will help you too!! : )
all your calc short videos save me alot of time! thanks Patrick
the first term would be pi/27; just plug n=1 into the very original series to get that value
At most universities or colleges, series occurs in your second semester, (Calc 2.) Diff EQ is traditionally meant to be taken after calc 3. However due to the gross similarities in the topics, such as trig, hyperbolic, and series, it is sometimes recommended to take Diff EQ right after calc 2. I have had several professors suggest this to me.
a decade later, still proving useful. Thanks mang
Always feels reassuring watching your videos. I was wondering what would drive you to make all these videos, but then again I see how many views per video you get, so no wonder : ).
when i first started making them, there was no monetization at all (for the first few years) i simply did it to help people cause i felt that is the right thing to do. i still make videos for that reason, getting a paycheck is an added bonus.
Thanks for sharing.
You are a Godsend to the world of math!
@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.
You're much more coherent than my professor, thank you so much. You're a great help!
@KillerZero259 i do allow for donations on my website. feel free to go make one :)
your videos are a life saver
This all makes so much more sense now. Thanks.
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!!!
@R0kmyS0X just a web site, check it out and do a search of ' sequences and series ' in the course list.
@McBirdec i also have free quiz / test materials on nixty with solutions to the problems if you are interested
thanks!
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!!!!
10 years later and it's helping me a lot
@smilerLFC glad you like the vids : )
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
Excellent job my mentor
YOU ARE A LIFESAVER
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.
thanks a lot patrick ...you save me every single day man
Extremely Helpful video thank you, you are an angel
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!!
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!!
@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.
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
Which video comes before this, sequentially? I cannot find a basic "geometric series" intro that leads into this vid... Thanks!
PatrickJMT's stuff on Nixty is very useful. Do as he said and go there and search for sequences and series.
You are The best all time.
this may be off topic but I totally dig the way you write summation sigmas. It looks like an evergreen tree..
yes I had to say that!
thank u sir
He left us off on a cliffhanger OMG!
thank you sir!
I got more out of this 10 min vid than i did from 3, 50 min lectures
Very helpful to help study for my Exam. thanks for the upload.
probably i think most people will have a harder time with seq/series if it is the first time they have really seen it in much depth...
You are a great tutor, Thank You Patrick
Nice video!!! You really helped me understand a lot!!!
I believe that the n=3 is 10/9= 1.1111 not 20/9 = 2.2222. I did it along with the video. I don't know if anyone caught that. I entered it many times in my calculator and got 10/9. Great video btw! Helps so much
7:16 Would this be considered a geometric series?
Thank you patrick you're the best !!
Thank you very much. This helped me review for my final exams.
tip for everyone watch this in 1.5x speed saves you so much time
thats right
+Erick Shaffer wish it was faster
.. even at 2 times speed as i am using this as a refresher
Mythic Mike
loll
+Erick Shaffer can i just say, YOU ARE A GENIUS?!!??
How do you do that? Increase the speed?
when do you use the test for divergence? 1/2 does not equal 0, how do you know you have to take the limit?
that divergence trick just blew my mind!
This is awesome, you have saved my life. Thank you so much.
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?
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.
How is it that I sit throw hours of class and understand nothing yet watch your videos and everything makes sense!
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?
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
i noticed that i don't fall asleep to your videos, and when im in class i always fall asleep
my english is not good, but i can understand your tuturial! thanks you very much, it's very useful!
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....
He Has My Vote for damn sure
thx for the math videos, i just subscribed!!
Patrick! I had this silly test today ( at least it looked like so) one of the series asked to solve was: the serie from 1 to infinite of [ (1)/ ( (n+1)(n+2) ) ]
I took the limit and I had it converges to 0...
It's that OK? I mean, cos I could not see it as a geometric serie, cos i could not figure the R number...
Ill be waiting for your answer... jesus im nervous
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.
11 almost 12 years old and still better than 99% of teachers and textbooks nowdays