Prove that the series $\displaystyle a_n=\root n\of {n}$ starting with $\displaystyle n=1$ has its maximum at $\displaystyle n=3$, therefore afterwords it strictly decreasing. (I know that $\displaystyle \lim_{n\rightarrow\infty}\root n\of {n}=1$.)

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- Jan 26th 2009, 10:36 AM #1

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## n^(1/n)

Prove that the series $\displaystyle a_n=\root n\of {n}$ starting with $\displaystyle n=1$ has its maximum at $\displaystyle n=3$, therefore afterwords it strictly decreasing. (I know that $\displaystyle \lim_{n\rightarrow\infty}\root n\of {n}=1$.)

- Jan 26th 2009, 10:40 AM #2

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- Jan 26th 2009, 10:41 AM #3

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- Jan 26th 2009, 10:50 AM #4

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- Jan 26th 2009, 10:54 AM #5

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- Jan 26th 2009, 10:56 AM #6

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- Jan 26th 2009, 10:59 AM #7