极限，即为一个数列，使得，其中L为一确定的常数，亦即数列随着n的增加而趋近于L。

设，

对于任意的正实数，存在自然数N，使得当n>N时，有 ，

用符号来表示即

则称数列收敛于，记作。

In mathematics, the limit of a sequence is the value that the terms of a sequence "tend to". If such a limit exists, the sequence is called convergent. A sequence which does not converge is said to be divergent. The limit of a sequence is said to be the fundamental notion on which the whole of analysis ultimately rests.