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

liliy

absolute convergence , converge or diverge: n^2/2^n. sumation going from n=1 until infinity

  • one year ago
  • one year ago

  • This Question is Closed
  1. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\sum_{n=1}^{\infty} {\frac{n^2}{2^n}}\]

    • one year ago
  2. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    Check it with the following test : \[\lim_{n\to \infty} {\frac{u^{n+1}}{u^n}}\]

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

    how?

    • one year ago
  4. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    sr, it is \[\lim_{n\to \infty} {\frac{u_{n+1}}{u_n}}\]

    • one year ago
  5. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    with \[u_n=\frac{n^2}{2^n}\] here

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

    wats sr?

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

    i dont understand the formula ur using

    • one year ago
  8. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    this is d'Alembert test

    • one year ago
  9. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    if this limit < 1, the series is converge

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

    neverheard of that...aight

    • one year ago
  11. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    what is the test you studied?

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

    we did power, ratio?

    • one year ago
  13. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    It seems to be a ratio test :-? may be differ name, display ratio test here

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

    given sumation A sub n. let the ratio= lim n goes to infinity of absolute val of A sub n +1 / A sub n then if ratio<1 series Coverges Absloutely ratio>1, diverges ratio=1, try diff test

    • one year ago
  15. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    yes it is

    • one year ago
  16. liliy
    Best Response
    You've already chosen the best response.
    Medals 0

    so how do u write it out?

    • one year ago
  17. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\lim_{n\to \infty} {\frac{\frac{(n+1)^2}{2^{n+1}}}{\frac{n^2}{2^n}}}=\lim_{n\to \infty} {\frac{(n+1)^2}{2n^2}}=\frac{1}{2}<1\]

    • one year ago
  18. liliy
    Best Response
    You've already chosen the best response.
    Medals 0

    howo does thatcancel out?

    • one year ago
  19. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't understand what you say, but if this limit <1, you can deduce this series converges. Moreover, it is absolute converge because \[\frac{n^2}{2^n}>0\]

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

    how do you get that second part of the limit?

    • one year ago
  21. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\lim_{n\to \infty} {\frac{(n+1)^2}{2n^2}}=\frac{1}{2}\]???

    • one year ago
  22. liliy
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1336454779193:dw|

    • one year ago
  23. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    It means \[\frac{(n+1)^2}{2^{n+1}}.\frac{2^n}{n^2}\] That's Ok?

    • one year ago
  24. liliy
    Best Response
    You've already chosen the best response.
    Medals 0

    ya...now wat?

    • one year ago
  25. anhkhoavo1210
    Best Response
    You've already chosen the best response.
    Medals 1

    you see \[\frac{2^n}{2^{n+1}}=\frac{1}{2}\]

    • one year ago
  26. liliy
    Best Response
    You've already chosen the best response.
    Medals 0

    o.m.g. yes! wow. sorry im so slow

    • 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.