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mukushla Group TitleBest ResponseYou've already chosen the best response.3
Proof: For each positive integer \(n\ge2\) , let \(S(n)\) be the statement\[1.2+2.3+...+(n1)n=\frac{n(n1)(n+1)}{3}\] Basis step: S(2) is the statement \(1.2=\frac{2.1.3}{3}=2\). Thus \(S(2)\) is true. Inductive step: We suppose that \(S(k)\) is true and prove that \(S(k+1)\) is true. Thus, we assume that \[1.2+2.3+...+(k1)k=\frac{k(k1)(k+1)}{3}\] and prove that \[1.2+2.3+...+k(k+1)=\frac{k(k+1)(k+2)}{3}\] what to do now?
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.3
@tux make sense?
 2 years ago

tux Group TitleBest ResponseYou've already chosen the best response.0
You rewritten sum as \[\sum_{i=1}^{n1}i(i+1)=\sum_{i=1}^{n}i(i+1)+(n1)(n1+1)\] ? And then substituted n=k in induction step Then n=k+1 you got ((k+1)1)(k+1) k*(k+1)=\[\frac{ k(k+1)(k+2) }{ 3 }\]
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.3
this is how we got things done by induction We assume that \(S(k)\) is true and we want to prove that \(S(k+1)\) is true.
 2 years ago

tux Group TitleBest ResponseYou've already chosen the best response.0
Thank you. Now I can do it alone
 2 years ago
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