Power series representation, radius and interval of convergence (KristaKingMath)
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- เผยแพร่เมื่อ 23 มี.ค. 2014
- ► My Sequences & Series course: www.kristakingmath.com/sequen...
Learn how to represent a function as a power series and then find the associated radius of convergence and interval of convergence of the power series.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingmath.com
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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingmath.com
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This has got to be one of the best tutorials on this stuff out there. So ridiculously easy to understand. Love how you break everything down. You've really helped me do well in calc 2. I am forever grateful.
+Nate Miller I'm so glad you liked it! Thanks for letting me know Nate!
thanks a lot krista it was far better than my mam taught me...and i understood all of it.
You are actually Queen Krista King ... thank you for making it so easy!
You're welcome, tzarrin, I'm happy to help! :)
Best explanation ever. Krista clear like your name. Thanks for doing what you do best
Thanks, Moe! :D
Phew - best math teacher on TH-cam.
Aw thanks! I'm glad I can help!
Phew - this one took a couple rewinds to keep straight for a weekend math warrior, but Krista's Clarity is still there to be the best of assistance. (Now, if I can only remember what the Radius Of Convergence is... No worries - can always go back to that video and replay.) Thank you Krista.
Your voice is heavenly
OMG!!! BRILLIANT!!! ABSOLUTELY BRILLIANT! I thought I would have to be inventive when trying to find the respective series for a function. Thank you!
You're welcome, I'm so glad it helped!!
Hands down, this is the best video I have found on Power Series Representation of Functions. Thank you so much for the thorough explanations!
Thank you so much!
I swear I am the worst student out there u can find but u have explained this concept so well that I understood it upon the 1st view! Thank u!
😊
incredibly helpful KRISTA
:D
Your video is the best explanation for power series that I've seen! :D
You are better than Sal. You are such a good teacher. Thank you very much.
I'm glad you like my style! :)
you are more than mathematician the expert that never ever seen before thanks a lot lady this is more than helpful
Hamisi Wenge So glad I could help!
how can I become th bst math teacher just like you
Great and clear explanation. Keep doing what you're doing.
Thanks, Hal! :)
I love your tutorials so much! I always watch them as a revision of what I've already learned and they always help me solidify my knowledge! Thanks a lot!
+agyness155 You're welcome, I'm so glad they're helping!
Krista, I really enjoyed your tutorials!
Thanks Nathan!
This helped so much!!! thanks!!!!
You are amazing (period)
a very detailed and yet a simple explaination, thank you so much, you helped me out in my calculus 3 :)
Thank you so much for this. You are the best!!
Hello again (the guy who's taking Calc 2 in Maymester), I just want to let you know that this is the only video that made me fully understand the power series. I tried PatrickJMT and Khan Academy but your videos are SO much better! You explain it more in detail and I just like your ways of teaching. I will need your videos for Calc 3 in two weeks lol!
I'm so glad you like my style! I'm happy I can help along the way! :D
wow!! such a great video, well explained
you are such a great teacher!!! My AP calc BC exam is in 3 days, and I've been watching your videos to help me get prepared. They are very helpful!
+Huy Bùi Lê Thank you so much, I'm glad they're helping! I hope the BC exam goes great... I'll keep my fingers crossed for you!
Great video, less random talking which is great. I was stuck in my assignment :), keep doing it
Thanks, glad it helped!
You are welcome, I have 2 questions that are giving me hard time here:
Determine the power series representation of f(x)=(x/(2-x))^3.
Find the sum of the series: (-1)^n/(2n+1)3^n
If you can do an example similar to it, I will appreciate it
Great as usual. I'm becoming your fan Krista !! : )
I'm honored! Thank you so much! :D
Very good example problem and thorough explanation!
Thank you so much!
So glad I found this right before finals! Great teacher!
Thanks! Good luck on your finals! :D
wow.... you are the best!
You are beyond helpful. Thank you, way to rock!
+Alicia Miranda Thank you so much, I'm happy to help!
really appreciate the effort and step by step explanation.. i understood this really easy, no confusion, no doubt no problem. Salute
Thanks, I'm so glad it made sense!
This was so helpful!!! You ROCK! :)
Hey thanks! I'm so glad it helped!!
I was totally lost with this, thank you!
Yay! Glad I could help!
That was a really nice explanation, thanks!
You're welcome!
Amazing!! thank you so much!! this helped me understand a lot of things i could not grasp from my professor.
I'm glad it could help!
Oh wow! This is really helpful. Thanks a lot.
Yay! You're so welcome. Glad it could help. :)
You are awesome! Thank you for your help!
+jack lo You're welcome, I'm so glad it helped!!
Excellent technique and explanation!
Thanks, Rajendra, I'm so glad you liked it!
+Krista King You are welcome. I like the way you explained what were double and triple integrals. You demonstrated a clear and in-depth understanding of the concepts. And you worked through the power series differentiation example pretty well.
muchas gracias
This is a great video, and I love how you used Algebra combined with the G.S.T. for the Interval of Convergence, rather than resorting to another test. I will keep that in mind going forward. Well done, and thank you.
P.S. Subscribed, and you're up there with Khan and PatrickJMT.
+bdgrey Thank you so much!
perfect explanation thanks a lot
+Rubens Távora Glad you liked it!
WOW THNX U SAVE MY LIFE
I'm glad it helped!!
Sos la mejor!! 😉
when you find the power series, doesnt it represent a geometrical series? So that u can take (-x^2/9) as r. And so u can prove its convergence by comparing (-X^2/9)absolute > 1 ? As this gives the same comparison as at the end of the absolute convergence test.
thanks. i have a test in a few hours so this helps
I am studying in Taiwan and usually am pretty confused in class. Your tutorials are the reason I am actually going to finish this degree haha keep up the awesome work! pleaseee :)
+Adriel Francois I'm so happy I could help!! :D
Five years later and I'm in the same position! 😭
Firstly, great video. Very clear step-by-step instruction. However I have a question. f(x) was rearranged so that is was in the form 1/1-x. We get 1/1-(-x^2/9)
From this do we not conclude instantly that the ratio is -x^2/9 and we can therefore apply the ratio test at this point and show that the interval of convergence for the power series is -3 < x < 3 ??
I'm not sure why we needed to go through the tricky algebra of a^(n+1)/a^n in order to determine the ratio.
Or am I missing something??
Love your voice😘
Does it matter if the series starts at something other than 0? Especially for like the radius of convergence?
Is it required to test the end points for this series since we're finding a series representation of a Maclaurin series. The endpoints should always diverge, no?
help ful
I thought that if the limit of a sub n+1 over a sub n does not equal zero, the radius of convergence was the inverse of the limit? So the ROC should've been 1/3?
I have my final on Thursday.. I'm scared as shit.
I have my final today XD im scurred. Its 25% of my grade.
goo luck my friend!
life saver
😊
hey I need for you. Can you help me? I want to find the sum : n(n +1)x n power n?? pleseee
instead of using the ratio test, could we have used the geometric series test? (x^2/9)^n+1 ?
We use the ratio test to find the radius of convergence because the ratio test will show absolute convergence. Any other test will not do this. If the ratio test fails then we we would use another test to show conditional convergence (usually the test for alternating series; however, we could use other ones).
whoaaa cool handwriting
y''+cos(x)y=0 how can i solve it by power series plz help me
You explain very well, but it is a little bit boring when you detail that "1+1=2", I think someone who's watching this tutorial about power series, he already knows how to simplify trivial fractions...
whatever, thanks for making this video it helped me a lot.
+Artashes Aslanoff Glad it helped, and thanks for the feedback!
Why are you checking the endpoints? They won't work because the rule you used to create the original geometric series says that the geometric series converges only if the absolute value of x is less than one. Also you used the ratio test, which there's nothing wrong with it, but if you only have one series then you can just take the (-x^2)/9 ratio that you built the series with as your ratio since it's literally common ratio. Easy to understand video though, just more work than needed on some things.
I dont know, i feel like you should get your mouth a little away from the microphone and make your voice a little more formal. professional videos , i am a huge fan
+Omar nabil Thanks for the feedback, I'm so glad you like the videos!
I'm just gonna take the L for power series representations on the final. Not worth it lmao.
Sorry but you speak too fast for me. I have difficulties to understand you accustically
Ugh, you just wasted so much of my time! I didn't need to use the ratio test on the first summation! I can go straight to saying |(x^2)/9| < 1 And then I get |x| < 3 and THEN I have to plug in the x values and use the ratio test. Blargh! >:(
I had to get out the big eraser because of you. The big eraser!
I didn't mean to waste your time. The point of the video is to show how to reliably find the radius and interval of convergence, which we can only reliably do using the ratio test. That's why I took the time between 7:00 and 13:00 to cover that process. While you can use your shortcut for this particular series, you won't always be able to, so I wanted to make sure people know how to do this. I hate it when you have to pull out the big eraser... sorry about that! :)