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: n!(2x-1)^n from 1 to infinity

  • one year ago
  • one year ago

  • This Question is Closed
  1. abb0t Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    are you being asked to determine whether the power series converges or not?

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

    yes

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

    when simplified i got absolute value of (2x-1) Lim n--->00 n+1

    • one year ago
  4. abb0t Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    use ratio test. works about 75-80% of the time for most power series. and best test to use when you have factorials.

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

    i did that, but not sure if i am right..

    • one year ago
  6. abb0t Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[L = \lim_{n \rightarrow \infty}\left| \frac{ a_{n+1} }{ a_n } \right|\] if L <1 absolutely convergent, and thus convergent L > 1 is divergent L = 1 use different test. but it SHOULD work.

    • one year ago
  7. abb0t Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[L = \lim_{n \rightarrow \infty}\left| \frac{ (n+1)! }{ (2x-1)^{n+1} } \times \frac{(2x-1)^n}{n!} \right| = \lim_{n \rightarrow \infty }\left| \frac{ n(n+1)}{ (2x-1)(2x-1)^n } \ \times \frac{ (2x-1)^n }{ n } \right|\]

    • one year ago
  8. abb0t Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm sure you can finish it from here.

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

    so when simplified should be (n+1)(2x-1) right?

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

    so i pull the 2x-1 out and im left with the Lim n--->00 of n+1 ?

    • one year ago
  11. abb0t Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yep.

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

    thanks abbot!!

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

    Your series diverges everywhere except for x =1/2. You can do it by the divergence test, the nth terms does not go to zero, then the series diverges

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

    hey Elias, how did you figure that out?

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

    It is a power series. if \( x\ne \frac 1 2\), then n!(2x-1)^n goes to infinity with n, so the nth-term does not go to zero, so the series is divergent.

    • 11 months 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.