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Conceptual question regarding sum of series

  1. Feb 8, 2008 #1
    1. The problem statement, all variables and given/known data
    If the sum(a_n) and the sum(b_n) are both divergent, is the sum(a_n + b_n) necessarily divergent?

    3. The attempt at a solution
    At first I thought it must be divergent, but then I asked, what if a_n is 1/n and b_n is -1/n... then their sum would be 0.

    Does this logic make sense? And if so, would it imply that sum(a_n + b_n)=0, and is therefore convergent?
  2. jcsd
  3. Feb 8, 2008 #2

    Gib Z

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    Homework Helper

    Your logic is correct. We can even get simpler examples. a_n = n, b_n = -n. Each diverges individually, but a_n + b_n = 0 for every term. And yes, it implies the sum of (a_n + b_n) is 0, convergent.
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