## Calculus 8th Edition

(a) A sequence {$a_n$} bounded if it is bounded above by $M$ , that is, $a_n\leq M$ for all n; and bounded below by $m$ that is, $a_n\geq M$ for all $n$. (b) A sequence {$a_n$} is monotonic if it is either increasing that is, $a_{n+1} \gt a_n$ for all $n$ or decreasing that is, $a_{n+1} \lt a_n$ for all $n$ (c) A bounded monotonic sequence converges . A sequence {$a_n$} converges means its limit ,as $n \to \infty$ exists. That is, $\lim\limits_{n \to \infty} a_n=L$
(a) A sequence {$a_n$} bounded if it is bounded above by $M$ , that is, $a_n\leq M$ for all n; and bounded below by $m$ that is, $a_n\geq M$ for all $n$. (b) A sequence {$a_n$} is monotonic if it is either increasing that is, $a_{n+1} \gt a_n$ for all $n$ or decreasing that is, $a_{n+1} \lt a_n$ for all $n$ (c) A bounded monotonic sequence converges . A sequence {$a_n$} converges means its limit ,as $n \to \infty$ exists. That is, $\lim\limits_{n \to \infty} a_n=L$