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Properties of summation

  1. Feb 7, 2010 #1
    If I have ∑(k xi + j yi)...how will I apply the distributive law on it?...I mean how do you split this notion?
     
  2. jcsd
  3. Feb 7, 2010 #2

    tiny-tim

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    Hi dE_logics! :smile:

    ∑(k xi + j yi)

    = ∑(k xi) + ∑(j yi)

    = k ∑(xi) + j ∑(yi) :wink:

    (if the ∑ is over infinitely many terms, you may have to be careful about convergence …

    but if for example all the terms are positive, then there's no difficulty :wink:)
     
  4. Feb 7, 2010 #3
    So we wont get ∑(k xi) + ∑(j yi)...that was too a possibility.

    So let's take an e.g. -

    x1 = 1, x2 = 2, x3 = 7, x4 = 1
    y1 - 19, y2 = 8, y3 = -10, y4 = 0
    k = j= 3

    ∑(k xi + j yi) gives -30

    k ∑(xi) + j ∑(yi) = -30

    and

    ∑(k xi) + ∑(j yi) = -30

    So both of the solutions are true...does everyone agree?...I mean -

    ∑(k xi) + ∑(j yi) = k ∑(xi) + j ∑(yi)
     
  5. Feb 7, 2010 #4

    HallsofIvy

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    ??Yes, we will, that was Tiny-tim's first step! But you asked about the distributive law and that hasn't been used yet, so then he factored k and j out.

    Yes, of course.
     
  6. Feb 7, 2010 #5
    Oh...I didn't see that...thanks.
     
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