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

 Aug 15, 2021
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By Cauchy-Schwarz, the minimum vaue is n/(n + 1).

 Aug 15, 2021

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