A real sequence is a function whose domain is the set of positive integers and range is a subset of the set of real numbers, i.e.,
Example:
Let , then
is a sequence in
.
Limit of Sequence:
Definition:
We say that a sequence of real numbers converges to a real number
if for every
there is an
such that
i.e., a sequence
converges at all it has to converge to a unique real number
which we call its limit, we express this by
where the symbol stands for approaches or tends to.
Properties:
If and
then,
Where