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education/math/MATH1220 (calc II)/Sequences.md
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@ -20,4 +20,5 @@ and say that $a_n$ *converges* to $L$. If no $L$ exists, we say $\{a_n\}$ *diver
3. $a_n b_n \to LM$ 3. $a_n b_n \to LM$
4. $\frac{a_n}{b_n} \to \frac{L}{M}$ holds true where all values are defined 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 $c_n \to L = M$ 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