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sasogeek
Group Title
prove by induction that
\(\large 1 \times 2 + 2 \times 3 + ... +n(n+1) = \frac{1}{3}n(n+1)(n+2) \)
 one year ago
 one year ago
sasogeek Group Title
prove by induction that \(\large 1 \times 2 + 2 \times 3 + ... +n(n+1) = \frac{1}{3}n(n+1)(n+2) \)
 one year ago
 one year ago

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Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
well, where are you stuck i assume you should know the steps n=k, then n=k+1
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
Assume \(n=k\) is true \[1*2+2*3+...+k(k+1) = \frac{1k}{3}(k+1)(k+2)\] Prove \(n=k+1\) \[1*2+2*3+...+k(k+1)+(k+1)(k+2) = \frac{(k+1)(k+2)(k+3)}{3}\] \[\frac{(k)(k+1)(k+2)}{3} + (k+1)(k+2) = \frac{(k+1)(k+2)(k+3)}{3}\] Now, you can prove RHS = LHS
 one year ago

sasogeek Group TitleBest ResponseYou've already chosen the best response.0
ok i understand and have worked the up to the point \(\large 1* 2 + 1* 3 + ... + k+1(k+2) = 1 * 2 + 1*3 + ... +k(k+1) +k+1(k+2) \) \(\large = \frac{1}{3}k(k+1)(k+2)+(k+1)(k+2)\) then what?
 one year ago

RadEn Group TitleBest ResponseYou've already chosen the best response.0
for left side : k(k+1)(k+2)/3 + (k+1)(k+2) = (k+1)(k+2)(k/3 + 1) = (k+1)(k+2)(k+3)/3 same like right side
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
Well, you prove as I said above. Prove the LHS = RHS \[=>(k+1)(k+2)\left[ \frac{k}{3}+1\right]\]It should be straight forward now.
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
Just, some algebra and you're done!
 one year ago

sasogeek Group TitleBest ResponseYou've already chosen the best response.0
it's still blurry but i'll try to get it in a bit :)
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
Well, where are you stuck?
 one year ago

Mimi_x3 Group TitleBest ResponseYou've already chosen the best response.1
All you have to do here is: Prove the LHS that is: \[\frac{(k)(k+1)(k+2)}{3} + (k+1)(k+2) \] Is equal to the RHS: \[=> \frac{(k+1)(k+2)(k+3)}{3}\]
 one year ago

sasogeek Group TitleBest ResponseYou've already chosen the best response.0
ohh, thanks :) normal algebra takes off from there i see :) makes sense now xD
 one year ago
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