Limit of a sequence

Limits:

It is useful to have the following symbolic fractions when dealing with limits. Note that infinity means positive or negative infinity.
(1) infinity/finite = infinity
(2) 0/finite nonzero = 0.
(3) finite/infinity = 0.
(4) finite nonzero/0 = infinity.
(5) infinity/infinity = Do Algebra.
(6) 0/0 = Do Algebra.


Limit of a sequence:

as n. or has the limit L written as A sequence
If the limit L exists, then we say the sequence converges. If the limit L does not exists, then we say the sequence diverges.

such that We define a sequence to be a function where the domain is the set of all positive integers and the range is the set of real numbers.
In other words, a sequence is an infinite list of real numbers. i.e., a sequence of numbers is an ordered list of numbers.
In other words, a sequence is a list of numbers in a definite order
is the ith term of the sequence. such that


Notation:
(the sequence with the notation We refer to the sequence whose nth term is
(the sequence 1 over n; the a sub n). The second sequence in example above is
(the sequence 3). last sequence is