Since they are all power series, the root of the linear expression being raised to the nth power must be in the center of the convergence interval. That alone eliminates a lot of possibilities.
@HenningMakholm Sorry, I am not really acquainted with terms such as "disk of convergence". This is actually an online class, so the only way I can learn is basically through online math videos and resources such as this...lol
I don't really get the point of video lectures. They're impossible to skim quickly if you need to refer back to something, and waiting for someone to speak everything is much slower than just reading a transcript.
But I did skip most of the lectures when I studied, because they were just reproducing content from the textbook that I could read at my leisure instead.
@HenningMakholm: Haha. Our lectures are all completely silent. You know why? Because lectures are for lecturers to show off how well they can do stuff they have been doing all their life. By writing so fast that you get a cramp in your hand and can barely keep up with him.
Besides, I don't understand the idea of copying a book to the blackboard and then back onto paper while being disturbed by talking of others and sleepy because I have to get up early.
I got 95% on my last Calc. II exam and 32% on my last physics exam (the average was 35), it's ridiculous how capitalistic and apathetic college has become.
In a university organized for adults, the point is to give the students various possibilities to learn the subject matter, and then afterwards offer exams that allow the students to get a certificate that they did learn it. Sitting in on lectures is an offer, not something that benefits the lecturer. Why should he care that the students use other offers to learn from?
@HenningMakholm Yes, but it is frustrating that they force you to pay for something you are not going to use, such as worthless lectures of rambling professors.
@MrCryptoPrime: I think "rambling professors" is too general. Some of them are actually quite nice. If you say it like that it makes me feel sad for the very few nice ones.
@HenningMakholm Oh, damn...I pay $4,000 USD every semester (all by myself). A job inexperienced 20yr old in the big ruthless world trying to survive haha
And I'm quite sure that if the university could get a larger percentage of students to pass by using their resources on something other than lectures, they would. They're paid per course passed per student, after all.
@HenningMakholm: Thanks for letting me know there are other rational people who think the same. Actually, in many universities (US), the size of a class and the attendance rate might say something about the quality of teaching of the lecturer. So they punished me for their own interest.
@Matt No, I said I went to all my geology lectures above. I really do like that professor and several I have had in the past, but there have been a lot of really crappy ones in my opinion who are really inconsiderate of us.
For those fresh-graduated lectures/professors, I can understand their urge to gain tenure. But for those tenures who have even been a dept chair before, I don't understand why they need to care about their faces so much.
It varies a lot whether being a department chair is something to be proud of. At some places it just means "once lost the draw among the tenured faculty".
Ok, sorry got distracted. Back to that homework problem...for #3, I used the ratio test and got |(8x-6)/6|*lim|n+1|. Assuming I did that correct, this would imply that it converges to (-inf, inf)?
@Mr_Crypt: Two points. (1) You can't pull the constant out of the limit if the constant is 0. (2) Otherwise, you pull it out and you get infinity, so the ratio test is failed.
OMG, nevermind, I just understood what I have to do...wow!!!! Talk about overthinking the problem, I feel like such an idiot! Oh well...lol
Ok, I just have one more, then I think I will be able to do all the rest. Upload it in just a sec.
Using the ratio test I got: |x/9|*lim|(n+2)/(n+1)| = |x/9|*1 = -1<x/9<1 = -9<x<9. That obviously does not help me? What do they mean: "find a formula". A formula for what? The nth term?