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Ketaksamaan n variabel dengan koefisien di depan variabelnya

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$x_1,x_2,...,x_n$ merupakan $n$ bilangan real nonnegatif sehingga $x_1+x_2+...+x_n=1$. Tentukan nilai minimum $$\sqrt{x_1+1}+\sqrt{2x_2+1}+...+\sqrt{nx_n+1}$$

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