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May 12th, 2019, 11:14 PM   #1
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Limit with sequence

Evaluate $\displaystyle \lim_{n\rightarrow \infty} \frac{(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n})^ n }{n}$.

To write it in short-terms : $\displaystyle \lim_{n\rightarrow \infty}n^{-1}H_{n}^{n} \; $ , H is the harmonic series .
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May 13th, 2019, 01:03 PM   #2
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In general $\frac{x^n}{n}\to \infty$ for $x\gt 1$. Since the harmonic series diverges, the expression $\to \infty$.
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limit, sequence

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