수열 수렴 판정법

1. Direct Method (epsilon-delta)

$$\forall \epsilon > 0,\;\exists N \in \mathbb{Z}^+\quad s.t.$$

$$n>N\;\rightarrow\;|a_n-c|<\epsilon$$

2. Box Method

(i) Bounded below (above)

(ii) Monotone decreasing (increasing)

\(\rightarrow\) \(a_n\) converges.

3. Cauchy Criterion

$$\forall \epsilon>0,\;\exists N \in \mathbb{Z}^+\quad s.t.$$

$$m,n>N\;\rightarrow\;|a_m-a_n| < \epsilon$$