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 August 25th, 2019, 06:58 AM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 833 Thanks: 113 Math Focus: Elementary Math Average value Find the mean value of $\displaystyle a_n =\frac{1}{n} \;$, $\displaystyle n\in \mathbb{N}.$
 August 25th, 2019, 07:53 AM #2 Senior Member   Joined: Jun 2019 From: USA Posts: 386 Thanks: 211 It has to be zero, right? For any $\displaystyle 0 < \varepsilon < 1, \exists N = \lfloor \frac{1}{\varepsilon} \rfloor$ terms larger than $\displaystyle \varepsilon$, leaving an infinite number of terms smaller than $\displaystyle \varepsilon$. Thanks from idontknow
 August 26th, 2019, 09:03 AM #3 Senior Member   Joined: Dec 2015 From: Earth Posts: 833 Thanks: 113 Math Focus: Elementary Math $\displaystyle m=\lim_{n\rightarrow \infty } \frac{H_n }{n} =\lim_{n\rightarrow \infty } \frac{\ln(n)}{n}=0$. H is the harmonic sum .

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