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Homework Help: Messing around with summation operators

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm just not sure how to change the operators in summation, can anyone help?

    Let [tex]s_{n}=\sum_{k=1} ^n ((-1)^{k+1})/k[/tex]

    what is [tex]s_{2n}[/tex]?

    2. Relevant equations

    [tex]s_{n}=\sum_{k=1} ^n ((-1)^{k+1})/k[/tex]

    3. The attempt at a solution

    [tex]s_{2n}=\sum_{k=1} ^{2n} ((-1)^{2k+1})/2k[/tex]


    [tex]s_{2n}=\sum_{k=1} ^{2n} ((-1)^{2k+2})/2k[/tex]

    This is in order to figure out a series proof, I just think I am really naive.
  2. jcsd
  3. Dec 2, 2009 #2


    Staff: Mentor

    How would you write s5 as a summation (not expanded)? How about s10? Don't overthink this problem.
  4. Dec 4, 2009 #3
    Thanks! I guess I tried to overthink, I've just seen people do amazing things with summation sings and sequences, I just tried to imitate.
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