Power Series - Part 1 (radius and interval of convergence)

[@pinkybananas1]

youre literally the best person teaching this it is so compatible with how i learn ive watched so many videos and yours just click honestly thank you for existing and making this video

[@abdullahijaz92]

Your videos indeed always are helpful man, off to my calculus 2 exam feeling much more confidence. Thank you so much :)

[@ElvinJones1981]

You are an excellent teacher! Thanks a lot.

[@mp3boy3239]

@thetranquilpride if you try it with the alternating series test I don't think you get a conclusive answer. Plus, with the ratio test you know that x HAS to be less than 1. This doesn't hold true with alternating series. Correct me if i'm wrong though. Not completely sure about that last part.

[@jasonjkeller79]

@fanciful (-1)^n*(-1)^n*n can be rewritten as (-1)^(2n)*n which will always raise (-1) to an even power thus cancelling the negative and making it just 1*n=n, and the lim_n->∞ n=∞. It's a simple nth term divergence test, you can't apply L'Hopital because it's not a ratio of functions like lim_n->∞ f(n)/g(n).

[@xoMissMeliss]

In your first example, You use the ratio test and you get the absolute value of x as your answer. How do you know that it is smaller than 1?

[@silouette65]

I think the reason he posted the video is because many people learn aurally, as opposed to visually. So this helps them, though it is unfortunate that it does not help you. :( What I would suggest it that you just take in your work to your teacher, professor, tutor, etc, and have them walk through the steps with you, so you can have a more 'hands-on' experience, or at least as hands-on as you can get with math. :P

How do you know that you should apply ratio test and not alternating series test here?

[@fanciful]

Really great videos, thanks for posting these. In your sixth slide, when showing x=-1 converges/diverges, you state that lim n-inf (-1)^n* (-1)^n will always be 1. Is this true? I think that 1^inf is an indeterminate form and you would need to apply L'Hopital or show it a different way. Thanks again.

[@Imagine-j5g]

I think i got it. To me, the theorem used in books and other sources are to wordy and lenghty. Since we have an x at the end, by the theorem, then its centered at 0.

[@masterbeta1992]

can a root test be used?

[@macmos1]

Can you please make a video for the proof of The Convergence Theorem for Power Series and The Radius of Convergence of a Power Series?

[@Imagine-j5g]

How do you know its centered at zero???

[@ian.ambrose]

Thank you Professor.

[@gsdlacusxoxo]

because of the ratio test. to converge, x must be less than 1

[@spaikywiam]

thank you thats really great

[@Brentjr94]

yes it may

[@qwe12353]

it is the same as professor reads off the slides in lecture.

[@chriskras530]

Don't mean to seem like a douche or anything but this seems like I might as well just read what the text book says. If it was enough for me to just read what the text book says, do you think I would be on KZbin trying to learn calc?

[@xoMissMeliss]

OOH okay. so, you want to show that it converges by it being less than one.

[@Curtis2255]

u spelled "Ghandi" wrong

[@jjoshi16]

its spelled "Gandhi" not "Ghandi" lol. Ghandi means something else entirely in Hindi...

[@12thando34]

i dont think that made the vid any less helpful