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Sum of the sum of harmonic series?

  1. Nov 2, 2012 #1
    1. The problem statement, all variables and given/known data
    Does this converge or diverge?

    Ʃ1/(1+2+3+4+5...+n), as n---> infinity?


    3. The attempt at a solution

    I rewrote this into Ʃ(Ʃ1/n) (is it correct?).

    I figured that since Ʃ(1/n) diverges, then the sum of each partial sum most (obviously) also diverge.

    However, it appears I'm mistaken. Can somebody help?
     
  2. jcsd
  3. Nov 2, 2012 #2

    Ray Vickson

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    Is 1/(1+2) equal to (1/1) + (1/2)? Basically, you are claiming that the answer is yes.

    RGV
     
  4. Nov 2, 2012 #3
    oh crap. yeh you're right.
     
  5. Nov 2, 2012 #4
    1+2+...+n=n(n+1)/2,so compare with the convergent series 2/n(n+1)
     
  6. Nov 2, 2012 #5
    ahh thanks. i completely forgot that you could rewrite 1+2+3..+n into n(n+1)/2.. thx!
     
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