5.1 Introduction to sequences
Introduction to sequences
Lessons
Notes:
Note:
1. If a sequence has the limit $L$, then we can say that:
$\lim$_{n →$\infty$} $a$_{$n$}$=L$
If the limit is finite, then it is convergent. Otherwise, it is divergent.
2. If the limit of the sequences {$a_n$} and {$b_n$} are finite and $c$ is constant, then we can say that
i) $\lim$_{n →$\infty$} $(a_n+b_n)=\lim$_{n →$\infty$} $a_n+$$\lim$_{n →$\infty$} $b_n$.
ii) $\lim$_{n →$\infty$} $(a_nb_n)=\lim$_{n →$\infty$} $a_n$$\lim$_{n →$\infty$} $b_n$.
iii) $\lim$_{n →$\infty$} $ca_n=c$ $\lim$_{n →$\infty$} $a_n$.
iv) $\lim$_{n →$\infty$}$(a_nb_n)=$ $\lim$_{n →$\infty$}$a_n*$ $\lim$_{n →$\infty$} $b_n$.
v) $\lim$_{n →$\infty$} $[a_n$$\div$$b_n]$
$=\lim$_{n →$\infty$}$a_n$$\div$
$\lim$_{n →$\infty$}$b_n$$,$$b_n\neq0$.
3. If $a_n\leq c_n\leq b_n$ and $\lim$_{n →$\infty$} $a_n=$ $\lim$_{n →$\infty$} $b_n=L$, then $\lim$_{n →$\infty$} $c_n=L$.
4.if $\lim$_{n →$\infty$} $a_n=0$, then $\lim$_{n →$\infty$} $a_n=0$ as well.
5. We say that:
Where the sequence {$x^n$} is convergent for 1< $x \leq$ 1, and divergent if $x$ > 1.

1.
Overview:

2.
Finding the terms of a sequence
Find the first five terms of the following sequences. 
3.
Finding the formula for a sequence
Find the formula for the general term $a_n$ for the following sequences 
4.
Convergence and divergence of sequences
Evaluate the limits and determine if the following limits are converging or diverging.