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I Sum of harmonic progression

  1. Oct 25, 2016 #1
  2. jcsd
  3. Oct 25, 2016 #2


    Staff: Mentor

    Do you mean the phrase:

  4. Oct 25, 2016 #3
  5. Oct 25, 2016 #4


    Staff: Mentor

  6. Oct 29, 2016 #5
    I think this video makes every thing clearer, thanks jedishrfu
  7. Oct 29, 2016 #6
    Still i don't have any clue/answer for why there is no formula for sum of HP for n terms, and i am not able to open your link
  8. Oct 29, 2016 #7
    Are you asking why there is not a smart formula for the exact sum with k from 0 to n ? The wiki page speaks mainly of integer sum and the clever video of divergence and infinite sum, which are another things.
  9. Oct 29, 2016 #8


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    Science Advisor

    As n grows large, you have [itex]\sum_{k=1}^{n}\frac{1}{k}\approx \ln(n)+\gamma [/itex].
  10. Oct 29, 2016 #9
    there is a nice but not very useful formula :
    [itex]\sum_{k=1}^{n}{\frac{1}{{a}+{b k}}}=\frac{{\psi^{(0)}({{\frac{a}{b}}+{n}}+{1})}-{\psi^{(0)}({\frac{a}{b}}+{1})}}{b}[/itex] where [itex]\psi^{(n)}(u)[/itex] is the polygamma function
  11. Oct 30, 2016 #10
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