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Quick question about Ratio Test for Series Convergence

  1. Apr 13, 2015 #1
    1. The problem statement, all variables and given/known data

    This is the question I have (from a worksheet that is a practice for a quiz). Its a conceptual question (I guess). I understand how to solve ratio test problems.

    "Is this test only sufficient, or is it an exact criterion for convergence?"

    2. Relevant equations

    Recall the ratio-test: If {an}n∈N is a positive sequence and there is a number a < 1 such that eventually an+1 ≤ a then the series is convergent. If, eventually, an+1 ≥ 1 then the series is divergent.

    3. The attempt at a solution

    I would assume that it would be considered "only sufficient," since if the result yields a ratio of one, convergence cannot be determined, thus it is not an absolute criterion.

    Would this line of reasoning be correct?

    Thanks,

    Colton
     
  2. jcsd
  3. Apr 13, 2015 #2
    that sounds right. it's sufficient but not necessary because there are other ways to determine whether or not a series converges eg ##\sum_{n} \frac{1}{n^{2}}## is known to converge but the ratio test doesn't give any information about it.
     
  4. Apr 13, 2015 #3
    Sounds good, thanks!
     
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