A sequence of numbers has a limit of L if the numbers get
closer and closer to L as the sequence proceeds so that the
difference them and L approaches 0.
example, the sequence 1.5, 1.25, 1.125, …., in which
the nth term is 1 + (1/2)n, has a limit of 1. The terms of
sequence get closer and closer to 1 as n increases. The difference
between the numbers and 1 is (1/2)n and this tends to 0 as
The sequence 2.9, 2.99, 2.999, …, in which the nth term
is 2.99…9 with n nines, has a limit of 3. A sequence
of shapes can also have a limit. For example, the polygons
have their vertices at a distance of 1 unit from the center.
As the number of sides increases the polygons get closer and
closer to a circle.