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apple_pi

Sum of first n triangle numbers

  • one year ago
  • one year ago

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  1. apple_pi
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    How do we find this?

    • one year ago
  2. cwrw238
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    1,3,6,10.. is this the series?

    • one year ago
  3. apple_pi
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    yeah, the one generated by n(n+1)/2

    • one year ago
  4. cwrw238
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    right - i remember that now but i don't recall the sum formula

    • one year ago
  5. cwrw238
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    i can only suggest googling it

    • one year ago
  6. UnkleRhaukus
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    |dw:1345110210994:dw|

    • one year ago
  7. cwrw238
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    http://mathforum.org/library/drmath/view/56926.html

    • one year ago
  8. cwrw238
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    @UnkleRhaukus - good drawing

    • one year ago
  9. apple_pi
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    Yeah, but that's only proving what we get, not how to get there

    • one year ago
  10. cwrw238
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    yes - i see what you mean - it seems that its a guess, which is then proved by induction

    • one year ago
  11. nightwill
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    \[S_n=\Sigma \frac{n(n+1)}{2} = \frac{1}{2} \Sigma (n^2+n) = \frac{1}{2}(\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2})\] \[ =\frac{1}{12}(n(n+1)(2n+1)+3n(n+1)) = \frac{1}{12} (n(n+1)(2n+1+3)) \] \[= \frac{1}{12}(n(n+1)(2n+4)) =\frac{2}{12}(n(n+1)(n+2)) = \frac{n(n+1)(n+2)}{6}\]

    • one year ago
  12. apple_pi
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    How did you get the sum of n^2?

    • one year ago
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