Definition:Convergent Sequence/Notation

Notation
When $\sequence {x_k}$ converges to the limit $l \in A$ we can write:
 * $x_n \to l$ as $n \mathop \to \infty$

or:
 * $\ds \lim_{n \mathop \to \infty} x_n \to l$

This is voiced:
 * As $n$ tends to infinity, $x_n$ tends to (the limit) $l$.

Some use the notation
 * $\ds \lim_{n \mathop \to \infty} x_n = l$

This is voiced:
 * The limit as $n$ tends to infinity of $x_n$ is $l$.

Note, however, that one must take care to use this alternative notation only in contexts in which the sequence is known to have a limit.