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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 $(a_1+2a_2+\cdots+na_n)^2.$
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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 t...
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