Question
1 Find the radius of convergence of the power series with each of the following coefficients:(a) ak = k(b)ak = k!(c) ak = 2k(d) ak =e-k2 Find the sum of each of the followng power seriers:aC(-1)*z2k k=0(6) C(-1)*2* k=13_ Find the Maclaurin seriers representation of function f(2)2 + 1 f(z) =(a) f(z) = e2?(b) f(2) = sinh(2)
1 Find the radius of convergence of the power series with each of the following coefficients: (a) ak = k (b)ak = k! (c) ak = 2k (d) ak =e-k 2 Find the sum of each of the followng power seriers: a C(-1)*z2k k=0 (6) C(-1)*2* k=1 3_ Find the Maclaurin seriers representation of function f(2) 2 + 1 f(z) = (a) f(z) = e2? (b) f(2) = sinh(2)
Answers
Find the radius of convergence and the interval of convergence of each power series. $$ \sum_{k=1}^{\infty} \frac{(x+1)^{k}}{k(k+1)(k+2)} $$
Versions an interval? Yes. Restrooms. The limited scale purchase infinity ignore the negative ones of cakes or taking of civilian life. So just be next. Okay. Mhm Right. Two capsules. Three. Yeah. By two on victoria. All over next. Okay. So simplify everything here. The limit as infinity of X squared samples three. It's two cables to So that would take that limit. Escape approaches infinity. It's close to Syria, which is always less than one there for me inside the radius is equal to infinity. The interval of conversions going to be from negative infinity community.
Days of convergence? Yes. Right. So this first time acceptance. Yeah. Okay. Mhm took it Okay. Skin to Her two simplifies this to infinity on this is with explains to take out experts to to the cake. So now you are Step one. We got from one -1-1 having to to both sides. We have one is less than Excuse me. I just want to test those. X equals one negative one over cute. Yeah, birch. That was really serious. X equals three search. So this week coverage by Pacers, it's therefore our interval scrappy 23 council Something that a radius is equal to one.
We can't testify, just sort of condition packing. Yes. Okay. Security. Mhm. Camps has to be Yeah. One thanks. Okay. That's is your health yeah, considering Yeah.
Some conversions. Little courage is for these producers. Shoot tests. Women escape purchasing thing. I'm just here. What Fine. Yeah. Okay. Text plans to okay. Some simple minus the King's one for 1. Take this opportunity just here. Okay. Start with that. It's true. Lots of three in the bottom here. Therefore, experts to its last three tells us that three is right. Yeah, spending two sides negative one five. Let's test those countries. Examples. Native one. Yeah. K over. Okay, so stick walls submission of making a cake. She checked Rachel's X equals five. Mhm. Two. Mhm. Okay. It's just the solution carriage. Yeah. Therefore interval Russians.