# Limit of a Number Sequence

## Limit of a Number Sequence

Value to which the terms in a number sequence extend.

When a sequence has a limit, we say that it converges; if it does not, we say that it diverges.

### Examples

• The following sum has a limit of 0, because its terms can approach 0 as close as we like, while remaining positive; this sequence converges toward 0:
1, $$\dfrac{1}{2}$$, $$\dfrac{1}{4}$$, $$\dfrac{1}{8}$$, $$\dfrac{1}{16}$$, $$\dfrac{1}{32}$$, …
• The following sequence diverges, because its limit is infinite: 1, 3, 5, 7, 9, 11, 13, …