anonymous
  • anonymous
Sum of first n triangle numbers
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
How do we find this?
cwrw238
  • cwrw238
1,3,6,10.. is this the series?
anonymous
  • anonymous
yeah, the one generated by n(n+1)/2

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cwrw238
  • cwrw238
right - i remember that now but i don't recall the sum formula
cwrw238
  • cwrw238
i can only suggest googling it
UnkleRhaukus
  • UnkleRhaukus
|dw:1345110210994:dw|
cwrw238
  • cwrw238
http://mathforum.org/library/drmath/view/56926.html
cwrw238
  • cwrw238
@UnkleRhaukus - good drawing
anonymous
  • anonymous
Yeah, but that's only proving what we get, not how to get there
cwrw238
  • cwrw238
yes - i see what you mean - it seems that its a guess, which is then proved by induction
anonymous
  • anonymous
\[S_n=\Sigma \frac{n(n+1)}{2} = \frac{1}{2} \Sigma (n^2+n) = \frac{1}{2}(\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2})\] \[ =\frac{1}{12}(n(n+1)(2n+1)+3n(n+1)) = \frac{1}{12} (n(n+1)(2n+1+3)) \] \[= \frac{1}{12}(n(n+1)(2n+4)) =\frac{2}{12}(n(n+1)(n+2)) = \frac{n(n+1)(n+2)}{6}\]
anonymous
  • anonymous
How did you get the sum of n^2?

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