Need to solve $\displaystyle (\frac{2011}{n+1})^{n+1}<(\frac{2011}{n})^n $ Tried natural logs to get $\displaystyle log_e{ }2011<n(log_e(n+1)-log_e{ }n)+log_e(n+1) $ Stuck here Any ideas please?
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Perhaps cross multiply and cancel to get $\displaystyle 2011n^n<(n+1)^{n+1}$. This can be put in the form $\displaystyle 2011<(\frac{n+1}{n})^n(n+1)$. The right hand side is approximately $\displaystyle e(n+1)$ for large $\displaystyle n$.
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