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Definition.
sequence.
An infinite sequence of numbers
is a function whose domain is the set of integers
greater than or equal to some integer $n_0.$
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Definition. The sequence $\{a_n\}$
converges
to the number $L$ if, to every positive
number $\varepsilon$
there there corresponds an integer $N$ such
that for
all
$n > N,$
$\abs{a_n – L}\lt \varepsilon.$
If no such number $L$ exists, we say that $\{a_n\}$
diverges.
If ${a_n}$ converges to $L$ we write
$\lim_{n\rightarrow\infty}{a_n}=L,$ or simply
$a_n\rightarrow L,$ and call $L$
the limit of the sequence.
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Theorem.
sandwich theorem for sequences
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Theorem.
continuous function theorem for sequences
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Theorem 4.
l'Hospital's Rule for sequences
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