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Double sum (Sigma) problem

  1. Sep 14, 2011 #1
    The problem statement, all variables and given/known data
    [itex]\sum_{k=1}^{3} \sum_{j=0}^{4}k^{j}[/itex]

    The attempt at a solution
    so this above means:
    [itex](1+1^{1}+1^{2}+1^{3}+1^{4})*(1+2^{1}+2^{2}...)*(1+3....)*....[/itex]
    or
    [itex](1*1^{1}*1^{2}*1^{3}*1^{4})+(1*2^{1}*2^{2}...)+(1*3....)+....[/itex]
     
  2. jcsd
  3. Sep 14, 2011 #2
    It doesn't make a difference which order you do it in. You can see if you type the following in to matlab:

    syms k
    syms j

    symsum(symsum(k^j,j,0,4),k,1,3)

    or,

    symsum(symsum(k^j,k,1,3),j,0,4)

    the answer is 157 either way.
     
  4. Sep 14, 2011 #3
    so 1 more question
    [itex]\sum_{k=0}^{4} \sum_{j=1}^{5} (3^{k} + jk)[/itex]
    how to calculate this without Matlab.
    Should I transform it? (but have no idea how)
    or just have to put [0;4] for k, and [1;5] for j, and add everything ?
     
  5. Sep 14, 2011 #4
    You don't need to do a transform, if you start with the sum over j you will get

    \sum_{k=0}^{4} (3^k+1k+ ... 3^k+5k) = 0+ ...+ 3^4+20
     
  6. Sep 14, 2011 #5

    Ray Vickson

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    Science Advisor
    Homework Helper

    It means the second one (which = 157); the first would be product_{k=1..3} sum_{j=0..4} k^j = 18755.

    RGV
     
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