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August 25th, 2019, 06:58 AM   #1
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Math Focus: Elementary Math
Average value

Find the mean value of $\displaystyle a_n =\frac{1}{n} \; $, $\displaystyle n\in \mathbb{N}.$
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August 25th, 2019, 07:53 AM   #2
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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 $\displaystyle \varepsilon$.
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August 26th, 2019, 09:03 AM   #3
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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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