diff --git a/education/math/MATH1220 (calc II)/Sequences.md b/education/math/MATH1220 (calc II)/Sequences.md index 75df3c9..869de87 100644 --- a/education/math/MATH1220 (calc II)/Sequences.md +++ b/education/math/MATH1220 (calc II)/Sequences.md @@ -21,4 +21,4 @@ and say that $a_n$ *converges* to $L$. If no $L$ exists, we say $\{a_n\}$ *diver 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 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 + > For example, given the series $c_n = \frac{n}{2n+1}$, both the numerator and the denominator approach infinity at a similar rate. However, when the numerator and denominator are both multiplied by $\frac{1}{n}$, it becomes $\frac{1}{2+\frac{1}{n}}$, an equivalent sequence that more clearly converges on $1/2$.