Find the Taylor series, centered at c=6, for the function f(x)=1x. f(x)=∑n=0∞ __ . The interval of convergence is: ___

Answer 1

Hi! I've included a video answer which walks you through how to organize your work to get this (or any!) Taylor Series. The particular function you've asked about has a very simple reason for why its interval of convergence is everywhere, so if you need more support with determining intervals of convergence in general you might need to ask more questions or seek out additional resources; I think Paul's Online Math Notes is a solid starting point for these, check out the whatever sections are relevant to your class from the Integral Test to the Root Test at https://tutorial.math.lamar.edu/Classes/CalcII/SeriesIntro.aspx (he's got worked examples, practice problems and everything)

I know they recommend keeping our videos under 5 mins and my answer to your question indeed wraps up just before the 5 min mark, but I hope you don't mind I couldn't help but going into more general insight about how to understand the point of Taylor Series... especially since, despite having taught this for years, I've never actually memorized the formula =P I just am able to recreate it by understanding that structure! Feel free to stop watching after you've gotten your answer, but those tips are there for you now or in the future; any time you want to get a big-picture overview of why the formula for Taylor Series, you can start from the 5 minute mark on this recording.

Thanks for your question, have a great day!