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Let $a_1,$ $a_2,$ $\dots,$ $a_n$ 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,

 Aug 17, 2021
 #1
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By Cauchy-Schwarz, the maximum value is 1/n^2.

 Aug 17, 2021
 #2
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1/n^2 isn't correct 

 Aug 17, 2021

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