Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Requiem Group Title

Power series problem. (x-2)^n/(n^n) Find the radius and interval of convergence.

  • one year ago
  • one year ago

  • This Question is Closed
  1. aykayyy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i actually just learned this today lol..... try the ratio test!

    • one year ago
  2. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I did, but am not sure if I am doing ti correctly

    • one year ago
  3. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    I would do the nth root test?

    • one year ago
  4. aykayyy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\lim_{n \rightarrow \infty} \left| \frac{ a _{n+1} }{ a _{n} } \right|\]

    • one year ago
  5. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1375316023379:dw|

    • one year ago
  6. aykayyy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh yes @sarahusher is probably right! i didnt see the ^n.... the root test would work better

    • one year ago
  7. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok ill try that

    • one year ago
  8. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok i did the root test and got (x-2)/n

    • one year ago
  9. aykayyy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    then take the limit of that

    • one year ago
  10. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Yep!

    • one year ago
  11. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i pull the x-2 out, and the limit of (1/n) would be 0

    • one year ago
  12. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    exactly!

    • one year ago
  13. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but then i multiply the 0 by the (x-2) right?

    • one year ago
  14. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    which would give me 0 overall?

    • one year ago
  15. aykayyy Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yup

    • one year ago
  16. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    As limit < 1, the series will converge for every 'x'

    • one year ago
  17. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Im not sure how they are getting the interval of convergence which they are saying is from negative infinity to positive infinity

    • one year ago
  18. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Okay, I'll explain: So when finding the radius of convergence: We know that as the limit=0<1, the series is convergent for every 'x' So for any x for any 'x' you get (ie from -infinity to +infinity) the series will converge Using the limit that you have, you get to ROC = infinity which directly gives you the interval as -infinity<x<infinity

    • one year ago
  19. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Does that make sense?

    • one year ago
  20. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Everything else makes sense, but the ROC (x-2) Lim as 'n'-------> infinity of (1/n) = 0 0*(x-2)= 0 Im just not sure how the ROC is infiinty

    • one year ago
  21. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    'The radius of convergence' r is a 'nonnegative real number' or '∞' such that the series converges if [x+L] < r , here L is your limit So our limit is 0 so we want an 'r' such that all of our 'x'<r but 'x' always converges for x<r And we worked out before that x converges for all values (ie for all R - real numbers) So it's not so much a calculation to work this out, as opposed to seeing that no matter what your value the series will converge no matter where it lies along R

    • one year ago
  22. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1375317501046:dw| Think of it like a disc, no matter where your value of 'X' lies in the disc, for this example the series will always converge

    • one year ago
  23. Requiem Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ok that makes more sense now...thanks sara :)

    • one year ago
  24. sarahusher Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Okay, If anything isn't clear let me know :)

    • one year ago
    • Attachments:

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.