1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Convergence Or Divergence

  1. Apr 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Determine either absolute convergence, conditional convergence or divergence for the series.


    2. Relevant equations
    [itex]\displaystyle \sum^{∞}_{n=1} \frac{(-1)^n}{5n^{1/4} + 5}[/itex]


    3. The attempt at a solution
    It converges conditionally i know, but i can't figure out how.
    1. I applied the alternating series test and concluded that the series converges.
    2. I attempted to use the Ratio test for absolute convergence, but l'hopitals is just going in circles. i'm not getting anywhere; the limit n->∞ is ∞/∞.
     
    Last edited: Apr 5, 2013
  2. jcsd
  3. Apr 5, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you mean (-1)^n/(5n^(1/4)+5) try a comparison test with a p-series. The ratio test won't help you.
     
  4. Apr 5, 2013 #3

    Mark44

    Staff: Mentor

    Is this what you meant?
    $$\sum^{∞}_{n=1} \frac{(-1)^n}{5n^{1/4} + 5} $$
     
  5. Apr 5, 2013 #4
    thanks. i fixed it.
     
  6. Apr 6, 2013 #5
    how do i prove the p-series? use an integral test? i don't think my instructor will let us simply identify a p-series but wants us to rather prove it.
     
  7. Apr 6, 2013 #6

    Mark44

    Staff: Mentor

    A p-series (below) converges or diverges, depending on the value of p.
    $$ \sum_{n = 1}^{\infty} \frac{1}{n^p}$$
    Use the integral test, with f(x) = x-p, and look at cases for p < 1, p = 1, and p > 1. There might already be a proof of this in your book.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Convergence Or Divergence
  1. Converge or Diverge? (Replies: 5)

  2. Divergent or Convergent? (Replies: 17)

  3. Converge or diverge (Replies: 7)

Loading...