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Wind ithe radius of convergence, R, of the series.SnlFind the interval, L, of convergence of the series_ (Enter your answer using interval notation;)Subml Answer...

Question

Wind ithe radius of convergence, R, of the series.SnlFind the interval, L, of convergence of the series_ (Enter your answer using interval notation;)Subml Answer

wind ithe radius of convergence, R, of the series. Snl Find the interval, L, of convergence of the series_ (Enter your answer using interval notation;) Subml Answer



Answers

Find the radius of convergence and interval of convergence of the series.

$ \sum_{n = 1}^{\infty} n^nx^n $

Even the powers were is under sigh. Okay, One of Okay, Expo. Okay, so in this Christian and would you use the root test here? So I need to computer limit on the road. Ok, absolute make a king goes to infinity. Then we get Nico to the route. They end up our day, we cancel down and we haven't left with the absolute arrests I won over. Okay, Of thanks here and now SK goes to infinity. We will have this I on, uh when we have the inside here echo Gina's. Oh, and signed Azari. Cogen is zero. Therefore, this limited Coachella's Oh, and it's unrest monitor. And one, This one implies that we have the radius. You go Judah infinity and the interval it go to minus infinity to infinity.

Okay, So our radius of convergence, remember, Will you limit as n goes to infinity Absolute value of an over and plus one. These guys are R A in terms So this is going to be limit as n goes to infinity. Ah, see, just in over in plus one that's one. So our radius of convergence is just one for the interval of convergence. We want to see what happens when we plug in one into R sum and we want to figure out what happens when you plug in minus one into R sum So access minus one, then our terms they are just going to be minus one times minus one times in. So what is going to be something from in equals? One to infinity of n. So this is definitely going to diverge. And similarly, when X is equal to one, we're just going to have some from n equals one to infinity of minus one to the end times in. And that's still going to diverge because their terms are not even going to zero. So are in points are goingto be thrown out. Those aren't any good. So our interval of convergence we have to leave open like this interval of convergences interval from minus one toe, one open

The power stories under four months. One bound K expert three creative Anybody £27 k in understand. And we're understanding to the, uh, minus. Uh, thanks, Bela Tree of ah, three and on. Then we'll be 27 here and now about. Okay. So listen in did in his that geometrics trees so we can use their property in that romantic stories Teoh fight down. That doesn't will be convergent even only if no absolute of minus expert number 27. It would be smaller than one isn't even Only if the absolute expert three with more than 27 hasn implies that absolute of X. Must be a small and and three surgeon Begin. Uh, right here we go to three. On the interval, it will be for ministry to 31 including it in point.

Yeah, the coefficient of this policy res A. N. Equals my nurse one to advance power Over 4 to our hands. Power enhance the radius of convergence equals limits the absolute value miners war into it. Hands power over walter ends. Power times four tours there And plus once power over -1 to the M. class. Once power and they send this canceled. And there is a my nurse friend there this term and this term Mosul canceled. And there is a folder and has that limit is formed. And The interval convergences from zero miners 4-0 platform, Which is from Miners 4- four.


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