Editing Sequence (section)

=== Infinite limits ===

In calculus, it is common to define notation for sequences which do not converge in the sense discussed above, but which instead become and remain arbitrarily large, or become and remain arbitrarily negative. If <math>a_n</math> becomes arbitrarily large as <math>n \to \infty</math>, we write
:<math>\lim_{n\to\infty}a_n = \infty.</math>
In this case we say that the sequence '''diverges''', or that it '''converges to infinity'''. An example of such a sequence is {{nowrap|1=''a''<sub>''n''</sub> = ''n''}}.

If <math>a_n</math> becomes arbitrarily negative (i.e. negative and large in magnitude) as <math>n \to \infty</math>, we write
:<math>\lim_{n\to\infty}a_n = -\infty</math>
and say that the sequence '''diverges''' or '''converges to negative infinity'''.