❖ Power Series - Finding the Interval of Convergence ❖
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- เผยแพร่เมื่อ 5 ก.พ. 2025
- ( • Differentiating and In... )
Power Series - Finding the Interval of Convergence | Complete Examples Explained!
Description: In this video, I walk through two complete examples of finding the interval of convergence for power series. We use the ratio test to narrow down the interval and separately check the endpoints to ensure that they are included (or not) in the interval of convergence. Throughout the video, I'll show step-by-step how to test each endpoint, analyze the behavior of the series, and arrive at the correct interval. A perfect guide for anyone studying power series, series convergence, or preparing for calculus exams!
What You Will Learn
How to find the interval of convergence for power series.
Using the ratio test effectively to determine convergence.
Analyzing endpoints of the interval to confirm convergence or divergence.
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so true
It was surprisingly difficult to find a good power series interval of convergence video. The Khan Academy video on this topic for example immediately switches to working with geometric series instead. I found this video helpful.
now you know where to look first!
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I keep getting notifications for this comment! It seems Patrick is a popular guy, and that some of his fans have a beef with Khan Academy (at least jokingly). I used both Khan Academy and TH-cam frequently for help with upper-level calculus and probability/statistics, and found both sources useful-though sometimes one source or another would cover a niche topic the others touched only perfunctorily.
In any case, thanks again to Patrick, Khan Academy, and various other unnamed sources for helping me successfully complete certain university courses.
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Calc 2 struggle bus
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Nope, NJ why do you ask?
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cause what i do is not entertaining
Luckily, what you do is very important to those of us with an interest in math, where otherwise many of us may have given up already.
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cuz people like entertaining more than learning
patrickJMT Dunno man logic is interesting.
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Best of luck!
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Senior math major in college and still coming back to these vids, you da goat!
I often watch your videos when I start a new subject in calculus 2 (and did in calc 1 as well) and I can't stress enough how helpful it is. My calc 2 professor is one of the worst I've encountered, and without your videos, I feel like there is a good chance I would be failing this course. You present with such clarity, and reference the underlying knowledge so well, that I rarely walk away without lucidity--not to mention the fact that you present the same material in 1/5 the time. Thank you.
It's wild how you make more sense of this in a step by step (in clear English) video in 10 minutes than a math professor can in an hour and a half. Thanks!
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13 years ago you were doing nonsense calc, now look at you, you made it.
this chapter caused me a couple of hours of stress and frustration.
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Props.
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I just wanted to say that you are by far the most amazing math teacher that ever lived. used all your video's for my Calc. 2 test, got a A-. thank you
I have my last cal 2 test of the semester at 11 tomorrow. I have been watching your videos on powers series and Taylor/Mclaurin series for the past couple hours and then working examples like yours. Seriously, though, thanks so much for your videos. They really do help.
you are correct as some professors do feel this way.
however, there are also tons of profs (researchers and non-researchers alike) who are passionate and concerned with teaching.
it is hard to teach a group of apathetic people though... that is often the biggest challenge.
You write all the same steps as my calculus 2 teacher. The difference is, you actually make sense and explain what's going on at a perfect pace!
once you find the interval of convergence (you actually do not have to check the endpoints if the interval), simply take the length of the interval and divide by 2.
for example, if the interval of convergences was:
(-1,7], the radius would be:
[7-(-1)]/2= 8/2 = 4
Thanks bud, seriously you are a great teacher. The way you explain things makes it seem so simple. if you didn't make these videos I'd probably be a letter grade down.
I am not sure what ti feel when I understand a video of TH-cam more than my actual professor... Patrick you have been a lifesaver, well more of a gpa saver during my Calc 2 class.
youtube in an enigma : )
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I have learned more from you in that past 10 minutes than I did from my Calc 2 professor the past 3 weeks.
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I've learned my entire calculus curriculum from your videos. Thank you so much
I've spent my entire day watching your videos on series and have just about learned it entirely from you.
Due to your videos, for my last two calc classes (calc I and II) I have maintained the highest scores in my class. There are many other math videos etc on youtube but yours are ordered the best and have the most examples.
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no one in my class pay attention to our prof. b/c unlike our prof. we can rewind you over and over and u r great at explaining.
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it happens to the best of us : )
It's 2019 and i'm watching this 1hour before final
me also man)
Don't know what I would do without these!
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You saved many lives of students with bad teachers and tutors... THANK YOU!
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ha! sorry to scare you! i only posted the video yesterday and have not updated my website yet. : )
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Just want to say you are a true math genius. Greatly Appreciate the videos. I could honestly skip all of my lectures and still pass the tests much easier than learning from my professor!
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ha, thanks! :)
I was doing some hardcore studying for my calc 2 final but I had to come on here and say THANK YOU for making this video. This topic is so much simpler than my professor makes it out to be.
i dunno if he said this later in the video, but often the Root Test is needed instead of the Ratio Test to work out these kinds of problems.
Bump!
Miguel Machado i realize both approaches* are correct, however sometimes you can only use one of the methods.
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i am going to take all of that as one of the best compliments ever.
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wow cant believe your 10 minute videos teach me more than those long hours of lecture do.
I really appreciate. It was hard for me to compute for convergence but now I can do.
Thank you very much
Just wanted to say thanks for all the help!
thank you very much Mr. Patrick! God Bless You, and give you a peace and health.
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Thanks!!!!! You saved me in my calculus class.
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my final exam is after two days from now ... & you helped me alot
Thank you .... my teacher
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Thanks for putting the video up man i was having some trouble on Interval of Convergence...Thanks a bunch buddy
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20 minutes before exam 3! Thanks for the vid!
Thank you, Patrick, for the clear examples. Learning this would have been hopeless if I'd been left to rely upon the awful textbook and the lecture videos from my course.
in many ways this is a great complementary resource. you do a great presentations!
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University student here
You, good sir, are a saint
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Seriously Patrick thank you so much! I am in the middle of a summer term for my calculus 2 class and this has been difficult for me to understand. Thank you :D
This video helps me a lot, just this video make me clear about finding the intervals of convergences. Thanks a lot patrickJMT
I am taking calculus 2 with the best professor at my university but you my friend you BEAT "the best prof " !!!!!!
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by the way patrick you are a damn lifesaver. calc 2 was easy for me up until series. your videos make it all better :)
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Too informative for my jam exam for IIT
Great stuff! I didn't know how to interpret the result after the ratio test, but now I do. Thanks!
thanks man im passing calculus 2 because of your videos