A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Find minimum of : \sum_{k=1}^{n}a_{k}^{2}+\left(\sum_{k=1}^n a_k\right)^2. My teacher told me that I shoul use CauchySchwarz inequality. Any tips?
 2 years ago
Find minimum of : \sum_{k=1}^{n}a_{k}^{2}+\left(\sum_{k=1}^n a_k\right)^2. My teacher told me that I shoul use CauchySchwarz inequality. Any tips?

This Question is Closed

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \sum_{k=1}^{n}a_{k}^{2}+\left(\sum_{k=1}^n a_k\right)^2\] \[\left(\sum_{k=1}^n a\right)^2=\sum_{k=1}^n a^3\] So your question boils down to \[\sum_{k=1}^n a^2+ a^3=\sum_{k=1}^n a^2(a+1)\]

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0The link is the ()^2=(^3) proof

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Although that's not Cauchy Schwartz.

DDT
 2 years ago
Best ResponseYou've already chosen the best response.0I didn't realise that task has another assumption :\[\sum_{k=1}^{n}p_ka_k=1\]

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry, I forgot that a1 does not necessarily equal 1, a2=2 etc. forget what I've told you so far.

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality#Statement_of_the_inequality you want the final formula of this section

henpen
 2 years ago
Best ResponseYou've already chosen the best response.0Or do you think a1=1, a2=2 etc in this problem?
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
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.