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education/math/MATH1220 (calc II)/Sequences.md
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@ -18,4 +18,6 @@ and say that $a_n$ *converges* to $L$. If no $L$ exists, we say $\{a_n\}$ *diver
1. $a_n + b_n \to L + M$ 1. $a_n + b_n \to L + M$
2. $C*a_n \to CL$ 2. $C*a_n \to CL$
3. $a_n b_n \to LM$ 3. $a_n b_n \to LM$
4. 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