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apple_pi

  • 2 years ago

Sum of first n triangle numbers

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  1. apple_pi
    • 2 years ago
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    How do we find this?

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

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

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

  5. cwrw238
    • 2 years ago
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    i can only suggest googling it

  6. UnkleRhaukus
    • 2 years ago
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    |dw:1345110210994:dw|

  7. cwrw238
    • 2 years ago
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    http://mathforum.org/library/drmath/view/56926.html

  8. cwrw238
    • 2 years ago
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    @UnkleRhaukus - good drawing

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

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

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

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

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