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I have a sequence $x_n$ and I want to prove that $\sqrt[n]{x_n}\le\sqrt[n+1]{x_{n+1}}$ for every $n$. The problem is I don't know how to handle the transition from $n$ to $n+1$ in the exponent. Are there nice relations/estimations/bounds of $\sqrt[n+1]{x}$ given $\sqrt[n]{x}$? This seems like a logical place to start.

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    Since you "have" a sequence $(x_n)_{n\geq0}$ it would help if you could give us some additional information about this sequence. Maybe it is then possible to crank out additional information about the relation between $x_n$ and $x_{n+1}$.2011-07-24

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