Monotonicity

Monotone Sequence	$\forall n \in N$
Monotonically Increasing	$a_{n} \leq a_{n + 1}$
Strictly Monotonically Increasing	$a_{n} < a_{n + 1}$
Monotonically Decreasing	$a_{n} \geq a_{n + 1}$
Strictly Monotonically Decreasing	$a_{n} > a_{n + 1}$

Monotone Convergence Theorem

(3.16, 3.17)

$a_{n}$	Bounded	Not Bounded
Increasing	$n \to \infty lim (a_{n}) = sup (a_{n})$	$n \to \infty lim (a_{n}) = \infty$
Decreasing	$n \to \infty lim (a_{n}) = in f (a_{n})$	$n \to \infty lim (a_{n}) = - \infty$