Problem

Find a power series representation for the functi…

01:14

Problem 3 Medium Difficulty

Find a power series representation for the function and determine the interval of convergence.
$ f(x) = \frac {1}{1 + x} $

Answer

$$I=(-1,1)$$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 9

Representations of Functions as Power Series

Discussion

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Video Transcript

for this problem. What we can see is the form of this function is very similar, Teo. A function that we know, which is half axe. Oh, maybe they see J x Kowtow one Oh one ninety six. So it always knows the power. Siri's of Jacks is Howard Siri's Asik Oto Some nation off go from zero to infinity. Nice. Oh, ax to the talent. So there is in this case we notice as thanks ICO toe jay ninety six h is e kowtow while minus niner six So on the final is equal to one classics Wow! Well, then plastics is equal effects so they know all of them. I hear it. So the power series for affects Asik Oto Jay minus tax Because summation on go from zero to infinity of minus X So that's how you end You know this case What we get is some nation go from zero no to infinity enough minus one to the power own times Axe to the Palin on the next step is to find this interval of convergence to find the eighth is is into off convergence If we are If you are no so interwar of convergence for J Axe is actually and minus one. Why on DH I've actually kowtow J minus X so they can we can know as X is convergence in tow is also you're just flip exact Same. So what you got is also mention on the way. So if you don't know, that's probably a it's fine. You can use ritual test What God is Hey, mate. On go to infinity and plus man Absolutely Area off and placement O a n. So in this case, a m e equal to this Asik oto this serious? So what? We have ways as equal to minus one with the power and prestige Times X to the power and class one o r minus v. So how end times asked, however, so take its absolute value What a kite is minus one times x So is ICO tow absolute value of facts So they know a as a racial test. This one must be smaller than that and also X absolute value is all the smaller one and we get the same radio of concordance and into loft conversions. Lee, I don't

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