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

This Question is Closed

Mimi_x3Best 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_x3Best 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

sasogeekBest 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

RadEnBest 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_x3Best 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_x3Best ResponseYou've already chosen the best response.1
Just, some algebra and you're done!
 one year ago

sasogeekBest 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_x3Best ResponseYou've already chosen the best response.1
Well, where are you stuck?
 one year ago

Mimi_x3Best 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

sasogeekBest 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
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.