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

bahrom7893

For what values of r>0 does the series converge?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm wary of using the integral test before actually getting some advices: |dw:1330831400158:dw|

    • 2 years ago
  2. .Sam.
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

    • 2 years ago
  3. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    .Sam. yeah what? Sorry to sound rude, but what's the point of disappointing me? I got so happy when I saw that notification pop up.

    • 2 years ago
  4. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    @Mertsj can u take a look?

    • 2 years ago
  5. .Sam.
    Best Response
    You've already chosen the best response.
    Medals 0

    uh I got it from a calculator it says that its converge but I don't know how it solves, lol

    • 2 years ago
  6. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    @malevolence19 can u help?

    • 2 years ago
  7. .Sam.
    Best Response
    You've already chosen the best response.
    Medals 0

    sry for the disappointment :D

    • 2 years ago
  8. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    tnx for tryin sam

    • 2 years ago
  9. malevolence19
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, I think I can help you.

    • 2 years ago
  10. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    awesome

    • 2 years ago
  11. malevolence19
    Best Response
    You've already chosen the best response.
    Medals 0

    For convergence of a series using the ratio test we must have that: \[\lim_{n \rightarrow \infty}a_n \rightarrow 0\] And: \[\lim_{n \rightarrow \infty} \left| \frac{a_{n+1}}{a_n}\right|<1\] So: \[\lim_{n \rightarrow \infty} \left| \frac{r^{\ln(n+1)}}{r^{\ln(n)}}\right|=\lim_{n \rightarrow \infty} \left| r^{\ln(n+1)-\ln(n)}\right|=\lim_{n \rightarrow \infty} \left| r^{\ln \left( \frac{n+1}{n}\right)}\right| \rightarrow 1\] Means that the ratio test is inconclusive. We need to find another approach (I should have realized this wouldn't work, its a rational function :/)

    • 2 years ago
  12. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    @JamesJ help?!

    • 2 years ago
  13. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 2

    mal19 almost had it. If |r| < 1, then the limit of the ratio a_{n+1}/a_n converges to zero.

    • 2 years ago
  14. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    oh so that's it?

    • 2 years ago
  15. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    It's that simple? dang it and i'm sitting here with improper integrals!

    • 2 years ago
  16. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 2

    *correction: If |r| < 1, then the limit of the ratio a_{n+1}/a_n converges to a number less than 1. And then by that ratio test, the sum converges.

    • 2 years ago
  17. bahrom7893
    Best Response
    You've already chosen the best response.
    Medals 0

    U guys rule!

    • 2 years ago
  18. JamesJ
    Best Response
    You've already chosen the best response.
    Medals 2

    namely, it converges to |r| itself.

    • 2 years 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.