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How to calculate the limit of $(n+1)^{\frac{1}{n}}$ as $n\to\infty$?

I know how to prove that $n^{\frac{1}{n}}\to 1$ and $n^{\frac{1}{n}}<(n+1)^{\frac{1}{n}}$. What is the other inequality that might solve the problem?

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    Why not use the value of $\lim \bigl[(n+1)/n\bigr]^{1/n}$?2012-09-05

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