Category:Sequence of General Harmonic Numbers Converges for Index Greater than 1

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This category contains pages concerning Sequence of General Harmonic Numbers Converges for Index Greater than 1:


Let $\map {H^{\paren r} } n$ denote the general harmonic number:

$\ds \map {H^{\paren r} } n = \sum_{k \mathop = 1}^n \frac 1 {k^r}$

for $r \in \R_{>0}$.


Let $r > 1$.

Then as $n \to \infty$, $\map {H^{\paren r} } n$ is convergent with an upper bound of $\dfrac {2^{r - 1} } {2^{r - 1} - 1}$.

Pages in category "Sequence of General Harmonic Numbers Converges for Index Greater than 1"

The following 2 pages are in this category, out of 2 total.