Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
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
 11 months ago
 11 months 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
 11 months ago
 11 months ago

This Question is Closed

satellite73Best ResponseYou've already chosen the best response.1
\[\frac{1}{1x}=1+x+x^2+x^3+...\] \[\frac{1}{1+x}=1x+x^2x^3+...\] \[\frac{1}{1+2x^2}=12x^2+(2x^2)^2(2x^2)^3+...\]
 11 months ago

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

satellite73Best ResponseYou've already chosen the best response.1
you need a 2 inside the parentheses
 11 months ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Oh 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.
 11 months ago

MarcLeclairBest ResponseYou've already chosen the best response.0
I thought power series was just sum x^n
 11 months ago

MarcLeclairBest ResponseYou've already chosen the best response.0
well the representation
 11 months ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Well 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.
 11 months ago

satellite73Best ResponseYou've already chosen the best response.1
converges if \(2x<1\) i.e if \(x<\frac{1}{2}\)
 11 months ago

MarcLeclairBest ResponseYou've already chosen the best response.0
Ah So i just take it right away. Makes sense. Thanks a lot^^
 11 months ago

satellite73Best ResponseYou've already chosen the best response.1
also you should start your summation at \(n=0\) i think
 11 months ago

satellite73Best ResponseYou've already chosen the best response.1
to be more precise i guess if converges if \(2x^2<1\) but same answer
 11 months ago
See more questions >>>
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.