Limit of a sequence
Infinite limits

A sequence (x n, m) {\displaystyle (x_{n,m})} is said to tend to infinity, written

if the following holds:

Symbolically, this is:

Similarly, a sequence (x n, m) {\displaystyle (x_{n,m})} tends to minus infinity, written

if the following holds:

Symbolically, this is:

If a sequence tends to infinity or minus infinity, then it is divergent. However, a divergent sequence need not tend to plus or minus infinity, and the sequence x n, m = (− 1) n + m {\displaystyle x_{n,m}=(-1)^{n+m}} provides one such example.
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