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Find the function represented by the following series and find the interva of convergence of the series.3)2k2The function represented by the seriesThe interva of co...

Question

Find the function represented by the following series and find the interva of convergence of the series.3)2k2The function represented by the seriesThe interva of convergence (Simplify your answer: Type your answer in interval notation.)

Find the function represented by the following series and find the interva of convergence of the series. 3)2k 2 The function represented by the series The interva of convergence (Simplify your answer: Type your answer in interval notation.)



Answers

Find the function represented by the following series, and find the interval of convergence of the series. (Not all these series are power series.) $$\sum_{k=1}^{\infty} \frac{x^{2 k}}{4^{k}}$$

Siri's on the phone. X minus two about K over the three. Out okay. From one to infinitive. You noticed? Then we can ready standing Children from under X minus two. Armored deny that anybody Okay. And here we want to stand would of zero. So we can register, Angela starting from zero to infinity expense too. And then by our own, I totally about And we know the first time echo to one. So we will need to sub tender one from here. And this one is the form off. No 1/1 minus X because you're someone's commission expo. Okay, so we can replace it. Now you again. The one off one Manus X months to on the night that we managed one. And it's, uh, should get echo to the we can put them to the same commonly nominate. I would get a ny minus, X plus two on the night minus one. They were getting coaching 9 11 money. Thanks, Manasquan. And then we put them Jellison common denominator. And then we get go to nine minus 11 and then plus X there were getting coaching I X minus two on what? 11 minus x and from here further into well conversions. We know it is invalid for the actual of EC smaller than one and doesn't implies that this one hanging the one we need to support the X minus two hour ni must be smaller than one isn't implies that the absolute of expense to smaller than nine and isn't even realized. Ex Minister will be between manis nigh and the nine and isn't on some years actually be to down 11 on this one. B minus seven on this will be the interval. American fortunes. Yeah, and this would be looking for

The streets under farm exclaimed One hour okay from surge infinitely. And this one is a ah, in this kind. I'm the do you magic series and we can register into the submission of the X clamp. That's one about what you don't have about gay and isn't it? Were equal to the one hunger one minus X grabbed this one out. You even only if, uh thanks, Grandpa Disc One bound Jews monitor and one but this X graham bliss one choose always greater, he continued. One left for this series, near always divergent.

Someone how to pay for some. Go on to infinity. Every conduct you have the island under one minus X They were eco Judah minus so much in the expo Kor OK, from one to infinity and it's funded Funder X would be between the minus 1 to 1. And now therefore we modify live in a little to have the X squared off. Ah exclaimed about Okay, uh, I can bring the one at the far I'll sigh Okay from one to infinity so we can use this form here on then were echoed this one We're in cultural miners on land under one minus x square And therefore we should get this with me. Coach, you know, 1/4 times minus on land off no one minus X squared and it will be valid for, uh here we replace the X by the X squared. That's for it Will be ready for the absolute X square will be treating the man one, 21 And isn't Minister. The X gland will be on ways things one be Yeah, it's Montego Juno minus one. This well And therefore we get the function here that it would convert you and it interval convergence here

We call that it will have. Does much of the expo came from search infinity. Listen, we're equal to 1/1 minus X for the absolute X smaller than one. And now every play this X here by the square with them the X minus two. We had to do the same thing here as well. And then we can get the answer for this one will be their submission of the square. The X minus two about K from zero to infinity. Me coach, the 1/1 minus square. It'd thanks just you. And then we get a coach in a one off three minus skirted the ANC's and spell it for the square. The AK minus two absolute value will be smaller than one. And it implies that underscoring the X minus two must be between minus one and one isn't imply standards. Great, that the axe must be between the three and one. And this implies that I want X him must be Ah, between the, uh, with square everywhere. We should get this one. We go to the NY and one here. And this would be the interval two conversions And this will be the function here we're looking for here


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