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Double summation problems

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider any sequence a1, a2,..., an and the nxn array of values bij = aiaj. Which terms in the array are involved in the sums L = Ʃ(between i=1 and n)Ʃ(between j=1 and i) bij
    and U = Ʃ(between j=1 and n)Ʃ(between i=1 and j) bij?

    Also, by symmetry, show that L=U.

    2. Relevant equations


    3. The attempt at a solution

    I've just started this topic and the double summation is really confusing me. Any guidance or suggestions on how to approach this would be really useful thanks.
  2. jcsd
  3. Jan 29, 2012 #2


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    Just do a small example by hand. Use maybe a 5 by 5 array of bi,j .

    a1a1 a1a2 a1a3 a1a4 a1a5

    a2a1 a2a2 a2a3 a2a4 a2a5

    a3a1 a3a2 a3a3 a3a4 a3a5

    a4a1 a4a2 a4a3 a4a4 a4a5

    a5a1 a5a2 a5a3 a5a4 a5a5

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