Question

I'm trying to write a power series for (1+x)^-2. I have the radius of convergence and (-1)^(n-1), but I can't seem to get the right answer for a_n. Could someone please take a look at my work?

Answer 1

looks to me that you have the an's

Answer 2

1,2,3,4,5,6,...

Answer 3

Ah, so (n+1)?

Answer 4

\[\sum_{n=0}^{\infty}(-1)^{n}(n+1)x^n\]

Answer 5

:/ That's What I had. I entered (-1)^(n-1), and it said that's right. Radius == 1, That was good, too. So in the formula \[\sum_{n=1}^{\infty} (-1)^{n-1} a_{n}x^{p_n}\] I'm good according to the system until I get to a_n

Answer 6

if you are starting from n=1 then you would get ...

\[\sum_{n=1}^{\infty}(-1)^{n-1}nx^{n-1}\]

Answer 7

Ah. Ironic that power series have me feeling so powerless. :(
Do you have a textbook you prefer? We've been using Varberg/Purcel, but I can't say I'm getting very far with it.

Answer 8

when I teach it i use Stewart

Answer 9

What's the title?

Answer 10

calculus

Answer 11

it is a pretty standard text for calculus in college

Answer 12

a lot of people have problems with sequences and series

Answer 13

you can try looking over

http://tutorial.math.lamar.edu/Classes/CalcII/SeriesIntro.aspx

and see if that helps

Answer 14

Figures. :) When I finally figure all of this out, I'll write a follow-up and call it that. "Calculus. *Figures*. Thanks for your help (and encouragement).

I've helped to develop curriculum (not in math), and even taught for about 3 years. I agree that the subject matter is challenging, but I swear, they could make it *so* much less difficult.

Answer 15

I'm sure they could, but then it wouldn't be any fun for the professors ;)

Answer 16

Indeed. Last semester I did a ton of research into online STEM education. If what I found is accurate, then around 50% of STEM majors quit (in the US). I doubt there's anywhere near so much attrition among faculty. :) Thanks again.

Answer 17

50% sounds about right.

Answer 18

are you in school for a second degree?

Answer 19

Actually, I'm in for my first. I dropped out as a junior. I started in graphic design/illustration. I still love to draw, but not for a paycheck. That was around 20 years ago. Then I bumped into Khan Academy. Hoo-boy.

Answer 20

you and i might be around the same age then :)

Answer 21

Well seasoned, then. :) I've been a programmer for most of that time--self taught. So are you teaching at the university level, or high school?

Answer 22

university

Answer 23

Nice. I love teaching, but I'm already pushing it with the family doing a physics BS. I'm not sure I could handle the K-12 drama. I can barely handle the single teenager I've got (and she's really good).

Answer 24

yeah...you really couldn't pay be to teach young kids. The college ones are getting a little annoying

Answer 25

Agreed. It's a good thing I'm not grading their papers. Texting hasn't done them any favors. I tend towards overkill on research an preparation. If I were a writing teacher now, I'd probably be happy to see solid punctuation and grammar. I will say, though, that the chemistry and biology students here (University of Utah) have been very solid.

Answer 26

well that's good to hear.

Answer 27

time to sign off. good talking to you. wish you luck

-Z

Answer 28

Same here. Thanks again.