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Let a_1, a_2, ..., a_n be real numbers such that a_1^2 + 2a_2^2 + ... + na_n^2 = 1.  Find the maximum value of (a_1 + 2a_2 + ... + na_n)^2.

 Aug 16, 2021
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The maximum value is n.

 Aug 16, 2021

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