From ecdbdcc1f8c7bdb81792f46361f2d5ad6411e38b Mon Sep 17 00:00:00 2001 From: arc Date: Mon, 22 Sep 2025 14:31:22 -0600 Subject: [PATCH] vault backup: 2025-09-22 14:31:22 --- education/math/MATH1220 (calc II)/Sequences.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 39fb6ba..75df3c9 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -20,4 +20,5 @@ and say that $a_n$ *converges* to $L$. If no $L$ exists, we say $\{a_n\}$ *diver 3. $a_n b_n \to LM$ 4. $\frac{a_n}{b_n} \to \frac{L}{M}$ holds true where all values are defined 5. If $L = M$ and a sequence $c_n$ exists such that $a_n \le c_n \le b_n$ for all $n$, then $c_n \to L = M$ -6. If $a_n$ and $b_n$ both approach infinity at a similar rate, $\frac{a_n}{b_n}$ will approach an arbitrary value. This value can be found by rewriting $\frac{a_n}{b_n}$ in such a manner +6. If $a_n$ and $b_n$ both approach infinity at a similar rate, $\frac{a_n}{b_n}$ will approach an arbitrary value. This value can be found by rewriting $\frac{a_n}{b_n}$ in such a manner that the end behavior of the series is more easily identifiable + > For example, given the series $c_n = \frac{n}{2n+1}$, both the numerator and the denominator approach infinity