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[4]Find the radlus and Interval 0f convercence of the following power series: ng"(x-3y...

Question

[4]Find the radlus and Interval 0f convercence of the following power series: ng"(x-3y

[4] Find the radlus and Interval 0f convercence of the following power series: ng"(x-3y



Answers

Functions to power series Find power series representations centered at 0 for the following functions using known power series. Give the interval of convergence for the resulting series. $$f(x)=\frac{1}{1-x^{4}}$$

Calm down and we have the 1/1 minus X. And then the Siri's represents for dysfunction with me. The submission. Expel. Okay. Giggles from Serge Infinity and its value for the absolute of X smaller than one. And here it would replace this X here by the expel. Far you have to do the same thing here and here as well. Therefore, we had a function, if thanks you go to every condition is I have, uh, then f X equal to 1/1 minus expo. Far. It will go to the summation off the Expo for about okay from Serge Infinity. Then we get encouraging a expel four K from zero to infinity and smell it from the absolutely x more than one. And this would be the answer.

F Thanks a cultural tension in verse on the far X square You noticed that we do the crime that next in court, you know, one off one plus four x squared square. And now, by general willing to terms the the drifting off the four X squares were included in it. X and we're Kona. Ever have no 1/1 minus X. We could get a submission expert OK from surging unity. And it's well, it found an absolute of exported and one Now we need to get this one so illegitimate. Berry's ex nearby the miners for next square. I want you and then you get a black hair and a swell for again. The 1/1 plus four x squared our people and it was coaching the summer doldrums. Action today. Explain how. Okay. And it would be fitting that we have from being a 16 x power sixth in. I just think gay for her ex power for okay. And then it is valid for the, uh, minus far x square, Absolute square. Here. I'm Salevaa Lius monitored and one equivalent tuned. Ah ah! Minus four X square. Absolute pollutes more than one and it's given and through the absolute of X Square smiled and, uh, one out of far and we're given to the absolute ex wanted and 1/2. And now we want to make in, Ah, eight except Pius hands. So we were going to multiply everything here by the eight X So we should get now that eight x over the one plus four x squared square You were Eagle Jew and, uh, some mention from zero to infinity. We have a 16 k x for gay temps eight x So we should get a good, you know, from Sergio Infinite Day. And this one in Weird right? Is there in doing that, you Juba far. Okay, isn't would be the tuber three. Therefore again the expert for okay times when the truth about four plus three sorry and listen will be valid for absolute X more than half. And now it wouldn't do integrate on both sides. 50 de thanks we get isn't exactly will be the tension in verse in far X square. And then when we go to on the right Inside here again Doc Submission from zero to Infinity and Juba four covers three expel for capers One another four K plus one. And it will be blessed. Say here is will be valid for after the X wanted and 1/2. And they hear we need to find a bluesy. It will lend the X equal to zero on the letters I get equal to zero vehicle trips and get is Aarhus. Well, let's see the pharmacy. He could you zero. And then we can remove this one now and this will be voted fund. Uh, listen would be acceptably between the minus half to half and notice then and, uh, X equal to minus 1/2. It will be in, uh uh, convergence. So we will in corn here, so just give me the answer.

The function f x encouraging a tension in verse under for X square. You notice that the m prime the X go to 1/1 glass 16 expel for so we need to stick to this form now. Pretty calm down and have the 1/1 minus x. The series for his function will be Submission of the expert came from Serge Infinity is really it for the absolute of X more than one. So now we need to create the denominator. Now, if I wanted to replay this ex hand by the minus 16 expert far so well, there's something from this angle this exodus Well, and it means that one of the one blessed 16 expo far it will ico Judah summation off the minus 16 Expert for our K from search infinity. Therefore, we get any coaching A summation off the menace. One power, okay, Usually can run that. I said to about four. Ok, expect for okay. And then we have here were being ah, uh from Serge Infinity. And it's valid form the minus 16 x Well, for smaller than one. Something for the ah, absolutely. The expert for smaller than ah, no 16. So there's something for the X. Absolutely x moaner Dan no. To So from here we want to integrate on both sides. And then under the second sign him. We had examined the function f X and it could you that tension in verse under four X square. On the right hand side, we have the minus one. Okay, do about four game expel for gave us Kuangdi, running by the fog gave this one person constant. C now is fully for the absolute of tanks. It's mounted into you. Find this value. See here we need to let the X equal to zero and tension in Rosero Echo ju zero. So therefore we get a little psycho. 20 on the right hand side began Echo. Jealousy only therefore doesn't implies that we have Seiko Jizo. And a final answer for this one would be Don't in inverse under Far Square, was it? Coggiola summation from Serge Infinity minus one power. Okay, Jimbo. Far. Okay, expel for guy. The violin, my love for guy. Uh, that's one. And then it's valid phone. Uh uh. Ex between, uh, formalist studio here

In this question, given serious under form expert. You okay on our farm? About K, Because from going to infinity. Yeah, I noticed that we have no one. Ah, under Siri's under form, Uh, Expo. Okay, goes from zero to infinity and we're equal to the 1/1 minus X has funded for the actual of X monnet and one. And now let's try to modify dysfunctional little. So this raise here can be modified by the X square number four about Okay, there's some lunch. Infinity. So we can re registering to, uh uh, It would have. Uh huh. Every Afghanis it took one on. Then we have this one will be the summation off the search. Infinity. Then I have the X square. Other far power. Okay. And then we have do it minus one here. And notice that this one here and will it go? Jude? Uh, function here. Window. Uh, axe now will be echo to the X squared over phone that I was You have gone over one minus x squared on the phone. Just one. Then we should get now. Ah, we would then Judaism. Common denominator. We have a phone than four minus X squared, minus one that we have the from all over. Four minus X squared, minus one. Then we should get a good uniform on this X square. Good damage. It s incoming. The nominate that we have a far manners for us X square. And eventually we have the X squared over four minus x square. And this will be the function that we're looking for here. And fund interval convergence. Yeah, we have. We stand with this one and isn't implies that it would be invited for the absolute of the X Square. Our far will be smaller than one isn't implies. Done absolutely. X square will be smaller. And then for this implies that, uh, X square will be between the months. Foreign far solution means that X will be lead to in the minus two and two here and literally the inter firm The convergence now


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