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jackkim4 Group Title

Plz help! super challenging question... Evaluate: lim n->inf 1/n[(1/n)^9+(2/n)^9+(3/n)^9+...+(n/n)^9] p.s: i got 0...but i don't think that's right ...

  • one year ago
  • one year ago

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  1. UnkleRhaukus Group Title
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    \[\lim\limits_{n\rightarrow\infty} \frac1n\left[\left(\frac1n\right)^9+\left(\frac2n\right)^9+\left(\frac3n\right)^9+...+\left(\frac nn\right)^9\right] \]

    • one year ago
  2. jackkim4 Group Title
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    yes! it's not 0 is it...

    • one year ago
  3. UnkleRhaukus Group Title
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    well the last term looks like it will be one

    • one year ago
  4. sirm3d Group Title
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    1/10 is my answer. is it among the choices?

    • one year ago
  5. jackkim4 Group Title
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    i separated (1)^9/(n)^9 and factored out all the (n)^9. resulting in (1/n^10) in the front. so that (1/n^10) times (n)^9 the last term will cancel. which will b left with (1/n) and (1/inf) is 0. 0 times anything left in the [ ...] will be 0. right?

    • one year ago
  6. jackkim4 Group Title
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    how did you get 1/10????

    • one year ago
  7. sirm3d Group Title
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    \[\large \int\limits_{a}^{b}f(x) dx=\lim_{n \rightarrow +\infty}\sum_{i=1}^{n} f(a+i \Delta x)\Delta x,\quad \Delta x = \frac{ b-a }{ n }\]

    • one year ago
  8. jackkim4 Group Title
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    i has no idea wat the triangle stands for :'(

    • one year ago
  9. sirm3d Group Title
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    \[\left( \frac{ 1 }{ n } \right)^9+...+\left( \frac{ n }{ n } \right)^9=\sum_{i=1}^{n}\left( \frac{ i }{ n } \right)^n\]

    • one year ago
  10. jackkim4 Group Title
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    i think the way ur doing it is correct... ur using the rem. sum right?

    • one year ago
  11. sirm3d Group Title
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    \[\large \sum_{i=1}^{n}\left( \frac{ i }{ n } \right)^9=\sum_{i=1}^{n}\left( 0+i\frac{ 1 }{ n } \right)^9\]so a = 0, b=1 (delta x) = 1/n

    • one year ago
  12. jackkim4 Group Title
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    lol ,,,,

    • one year ago
  13. sirm3d Group Title
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    therefore \[\large f(x)=x^9\]\ YES, the problem is a riemann sum.

    • one year ago
  14. jackkim4 Group Title
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    so how did u get 1/10???

    • one year ago
  15. jackkim4 Group Title
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    got it

    • one year ago
  16. jackkim4 Group Title
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    ur my hero !!!!

    • one year ago
  17. sirm3d Group Title
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    ^^

    • one year ago
  18. jackkim4 Group Title
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    can u help me with next one when i close LOL i got an answer. but idk if i got it right...pretty plzzz

    • one year ago
  19. sirm3d Group Title
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    i'll try. pls post.

    • one year ago
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