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imqwerty

  • one year ago

find general formula of --> 1^x +2^x +3^x.........n^x

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  1. imqwerty
    • one year ago
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    @dan815

  2. anonymous
    • one year ago
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    \[\sum_{a=1}^{n}a^{x}\]

  3. imqwerty
    • one year ago
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    @MayankD i want to find formula like we have- \[\sum_{n=1}^{n}n^2 =\frac{ n(n+1)(2n+1) }{ 6}\]

  4. dan815
    • one year ago
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    hey

  5. imqwerty
    • one year ago
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    hey :)

  6. dan815
    • one year ago
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    oaky so if u noticed this u can rewrite this in some slightly different notation like theyre all just sum of sums

  7. dan815
    • one year ago
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    |dw:1443861264405:dw|

  8. dan815
    • one year ago
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    |dw:1443861345422:dw|

  9. dan815
    • one year ago
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    you see how these sums of sums is working

  10. dan815
    • one year ago
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    now can we get a general form for sum of sums formula

  11. imqwerty
    • one year ago
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    why did u say its =0N^2 ?

  12. dan815
    • one year ago
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    it means the highest degree for our closed formula is of degree 2

  13. imqwerty
    • one year ago
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    ok :)

  14. dan815
    • one year ago
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    jsut simplifying the math for now, we can worry about the additional order terms later

  15. anonymous
    • one year ago
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    Big-O is a function which defines an upper bound for another function

  16. anonymous
    • one year ago
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    Asymptotically that is

  17. dan815
    • one year ago
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    now lets thinking if there is some way of computing sum of sum of sum of sums...

  18. dan815
    • one year ago
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    |dw:1443861532777:dw|

  19. imqwerty
    • one year ago
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    cx

  20. anonymous
    • one year ago
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    I do not think you will get a simplistic answer like those you showed me for this variable exponential summation. The answer has to do with generalised harmonic numbers(courtesy wolfram alpha)

  21. imqwerty
    • one year ago
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    ye i saw that too :)

  22. dan815
    • one year ago
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    yeah xD i think this is why i stopped after i got the recursive equation to keep generating 1 degree higher

  23. dan815
    • one year ago
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    but hey i think there is still some ways

  24. dan815
    • one year ago
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    to get approximate solutions

  25. imqwerty
    • one year ago
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    http://prntscr.com/8n6roc

  26. dan815
    • one year ago
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    this stuff reminds me of this sigma function thing

  27. dan815
    • one year ago
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    which is used in arithmetic function stuff, and u do something called dirichlet convolutions

  28. dan815
    • one year ago
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    and i believe they are also formed out of the harmonic series

  29. dan815
    • one year ago
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    take a look at this if you are interested https://www.youtube.com/watch?v=X0XJ3TuMiFc

  30. Zarkon
    • one year ago
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    |dw:1443896724330:dw| this is not true

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