diff --git a/quarto/limits/sequences_series.qmd b/quarto/limits/sequences_series.qmd index ef3bc29..d3ca206 100644 --- a/quarto/limits/sequences_series.qmd +++ b/quarto/limits/sequences_series.qmd @@ -284,7 +284,7 @@ First we consider only sequences with non-negative terms. If $a_n \geq 0$ for each $n$ then a necessary condition that $s_n \rightarrow s$ is that $a_n \rightarrow 0$. ::: -This says if $a_n$ does not coverge to $0$ then $s_n$ diverges. It is definitely not the case that a sequence that converges to $0$ will lend itself to a convergent series. A famous example would be $\sum_{i=1}^n 1/i$ which diverges. The partial sums of this series are termed the [harmonic series](https://tinyurl.com/ua4893w5) and have the property that $s_n = \ln(n) + \gamma + 1/(2n) + \epsilon_n$ where $e_n \rightarrow 0$ and $\gamma \approx 0.5772$ is a constant termed the Euler-Mascheroni constant. (See `MathConstants.γ`.) +This says if $a_n$ does not converge to $0$ then $s_n$ diverges. It is definitely not the case that a sequence that converges to $0$ will lend itself to a convergent series. A famous example would be $\sum_{i=1}^n 1/i$ which diverges. The partial sums of this series are termed the [harmonic series](https://tinyurl.com/ua4893w5) and have the property that $s_n = \ln(n) + \gamma + 1/(2n) + \epsilon_n$ where $e_n \rightarrow 0$ and $\gamma \approx 0.5772$ is a constant termed the Euler-Mascheroni constant. (See `MathConstants.γ`.) :::{.callout-note appearance="minimal"}