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Homework Help: 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


    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


    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


    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.
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