Sequences

• Arithmetic Sequences
• Geometric Sequences
• Pattern described by $a_n$
• A sequence $\{a_n\}$ converges to the limit $L$ if for any $ϵ>0$, $\mathrm{\exists }N\in \mathbb{Z}$, such that $n>N⟹|a_n-L|<ϵ$

Limits

• If $a_n$ approaches $L$ as $n\to \mathrm{\infty }$, then the sequence $\{a_n\}$ is convergent, and $\underset{n\to \mathrm{\infty }}{lim}{a}_n=L$
• Even if it's bounded, if you can't actually define a value $L$, then the limit does not exist
• If you have a recursive formula, you can find $L$ by realizing that as $n\to \mathrm{\infty }$, $a_{\mathrm{\infty }}=a_n=a_{n+1}$, simply set everything to $a_{\mathrm{\infty }}$, and solve for it
• Otherwise, do Limits normally