9.9 Power Series

Run out of time?

If alternating series test does not work, you cannot say that it does not converges 🙄 it means no conclusion

Sir, your video is magic! I missed a few lectures for my math cal 3 so I don't understand my homework. I looked at the course notes but they were very dull! then I watched your video (this one and the root test one)! they are so clear and practical! I did my homework smoothly! (I even guessed some answers correctly by just imagine the pattern)

👌😌

يزاك الله خير 💛

your students are hella lucky D:

I luv you

Thank you so much! This has saved me on my Calculus 1 final!

ı learned that alterneting series test can only for detecting convergency ,so ı thought that you are not able to decide divergence for n^3 (-1)^n.Hence,ım confused pls help me,best regards.

does the limit ever not equal to 1

Thank you I was struggling to get in

This is woke. Thank you

Came back to brush up for power series solutions to differential equations, thanks Patrick!

Senior math major in college and still coming back to these vids, you da goat!

you are the best PatrickJMK........... FOR me you are just like Lionel Messi in maths...GOAT

patrick you're a certified beauty

Thank you SO much

Teaching yourself m***********?????

Trying to save myself before my calc BC ap test tomorrow, I think I know almost nothing.

Thanks a lot from india!👍

Arrasou

1 Question! So, when you have placed 4 , we got n^3=0 and thats not logically true what you have said in this video. I agree! But how it proves the Interval of convergnce between (4,6) that is 4<x< 6 ?

U give a awesome explanation it helped me alot thanks

2019??

It's 2019 and i'm watching this 1hour before final

Sir,plz solve the following sum- The series £n=1 to infinity n power 2 * x power n is uniformly convergent in [-α,α]

With all the insanity of online courses your videos are going to be the only reason I pass my exam. Thanks so much for making them! You really make the content easy to understand and follow

is there is anyone who is studying in mit

does the bracket ' { ' of ' ( ' shows one of it is true and other one is uncertain

thx g

Thank u so much sir for such simple explanation

❤️ from India

it's 2021 and my teacher assigned this video to us to learn from

And I don't even have a Calculus 2 in my University. But I gotta teach my student :)

Don't know what I would do without these!

20 minutes before exam 3! Thanks for the vid!

I LOVE YOU PAT <3<3<3

Treat this comment like a time capsule, someone lmk if they see this in 10 years

I was here around 5 years ago back in my community college. I am back with Patrick again with my FE Civil Exam. Patrick Thanks you so much for your help. You are the man

X

this video was uploaded a while ago but I'm taking ap calc bc right now and i have a test tomorrow on this topic and it was so confusing when it was originally introduced in class. after watching this video, it all makes sense!! thank you so so much you are a godsend

can't believe I am learning from a video filmed in 2008 in the year 2022

I found this video to be very helpful, Thank you.

Goat

helpful, thanks

Thank you so so much!! This was incredibly clear to follow. I have an exam coming up and was absent the day we were taught this & for once I'm feeling more confident in the material

Love from India 🙏🏻👍👍👍
Too informative for my jam exam for IIT

University student here

You, good sir, are a saint

You used the alternating series test to show that the series diverged at x=4, but the alternating series test can only show convergence. If either of the two criteria are not met, then the test can't be used, and another test must be used to show divergence or convergence. Amazingly, there are actually series which fail one or the other criteria, but which do converge. The simple Test For Divergence would have shown that the series diverges when x=4.