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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 $\displaystyle \varepsilon$.

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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