Definition:Convergent Sequence/Notation

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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.