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Homework Help: Infinite series question

  1. Apr 4, 2010 #1
    Given that the series from n = 1 to infinity of An converges to L, which of the following conclusions is valid for the series from n = 1 to infinity of (An)^2?

    A) It may diverge
    B) It converges absolutely
    C) It converges to M < L
    D) It converges to M > L
    E) It converges to M^2 = L

    My intuition tells me the answer is E). But I am not sure can someone help figure this out please
     
  2. jcsd
  3. Apr 4, 2010 #2
    Hints: convergent geometric series (this should eliminate some of the possible answers). Then look up what it means to converge absolutely, and play around with

    [tex]\sum_{n=1}^\infty \frac{(-1)^{n+1}}{\sqrt{n}}[/tex]
     
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