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Let a1,a2,a3,a4...an be real numbers such that \(a_1^2+2a_2^2+\cdots+na_n^2 = 1.\)Find the maximum value of \((a_1+2a_2+\cdots+na_n)^2\)

 

Thanks so much!

 Oct 22, 2021
 #1
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By Cauchy-Schwarz, the maximum value is n^2/4.

 Oct 22, 2021

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