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DDT
 3 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?
DDT
 3 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?

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

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

DDT
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0Or do you think a1=1, a2=2 etc in this problem?
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