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Homework Help: Summable Sequences

  1. Apr 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine whether or not the sequences below are summable:

    {(-1)^n}

    {(-1)^n + (-1)^(n+1)}

    {(-1)^n} + {(-1)^(n+1)}

    2. Relevant equations



    3. The attempt at a solution

    Okay, I'm having some trouble thinking about these the right way. Since

    {(-1)^n}= -1, 1, -1, 1, .... then its sum = -1, 0, -1, 0, -1.

    I think this means that it is not summable even though it is 0 every other term.

    Assuming it is divergent, then {(-1)^(n+1)} is of course also divergent... But I think that two divergent sequences added together might be convergent.

    But does it matter whether they are summed together as one sequence or two? Either way they will still = 0, 0, 0, 0, 0 .... right? So would they both be summable? Sorry if I sound confused - it's just because I am.
     
  2. jcsd
  3. Apr 11, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    … you can't add things if they don't exist …

    Hi alovesong! :smile:

    (it's ok so long as you know you're confused! :smile:)

    Yes it does matter.

    :smile: … you can't add things if they don't exist … :smile:

    ∑{An} + ∑{Bn} is only defined if both ∑{An} and ∑{Bn} are defined.

    Even though ∑{An + Bn} is defined! :smile:
     
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