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Update Math4111_L22.md

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2024-11-19 20:33:36 -06:00
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pages/Math4111/Math4111_L22.md
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@@ -71,9 +71,7 @@ $$
>
> $I(9)=\{1,2,\dots,9\}$, $J(9)=\{1,2,4,3,6,8,5,10,12\}$, $I(9)\backslash J(9)=\{7,9\}$, $J(9)\backslash I(9)=\{10,12\}$.
>
>$$
|s_9 - t_9| \leq |a_7|+|a_9|+|a_{10}|+|a_{12}| \leq \sum_{k=7}^{12} |a_k| < \epsilon
$$
>$$ |s_9 - t_9| \leq |a_7|+|a_9|+|a_{10}|+|a_{12}| \leq \sum_{k=7}^{12} |a_k| < \epsilon $$
This proves that $\lim_{n\to\infty} |s_n - t_n| = 0$.