A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
How can you rewrite the function as a power series?
f(x) = x/ (1 + 2x^2)
I know I have to take out the x so x ( 1 / (1 + 2x^2)
however I'm stuck afterwards
anonymous
 3 years ago
How can you rewrite the function as a power series? f(x) = x/ (1 + 2x^2) I know I have to take out the x so x ( 1 / (1 + 2x^2) however I'm stuck afterwards

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{1}{1x}=1+x+x^2+x^3+...\] \[\frac{1}{1+x}=1x+x^2x^3+...\] \[\frac{1}{1+2x^2}=12x^2+(2x^2)^2(2x^2)^3+...\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So would I write the sum as \[\sum_{n=1}^{\infty} (1)^{n} (x)^{2n+1}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you need a 2 inside the parentheses

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Oh yeah my bad. But how can I find the radius of convergence if I can't use the ratio test afterwards? I mean there's no division going on. Only thing I can think of is the root test but its negative, so the root test won't work perfectly.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I thought power series was just sum x^n

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well the representation

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Well I took the x and added it to the 2x^(2n+1) because the x was "outside" of the sum. So i just added it and thats what I did. I don't feel like writting the equation. I don't know if you follow what I'm saying.It was my guess really.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0converges if \(2x<1\) i.e if \(x<\frac{1}{2}\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ah So i just take it right away. Makes sense. Thanks a lot^^

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0also you should start your summation at \(n=0\) i think

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0to be more precise i guess if converges if \(2x^2<1\) but same answer
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.