Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

mukushlaBest 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?
 one year ago

tuxBest 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)=\[\frac{ k(k+1)(k+2) }{ 3 }\]
 one year ago

mukushlaBest 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.
 one year ago

tuxBest ResponseYou've already chosen the best response.0
Thank you. Now I can do it alone
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.