## Sequences

A sequence is a function whose domain is the set of positive integers. The contradiction of a sequence will be considered the set of real numbers.

Each positive integer "n" corresponds to a real number *f (n)*.

** **

The_{1} = f (1); The_{2} = f (2); The_{3} = f (3);…; The_{no} = f (n)

### Notations

{The_{no}} = {a_{1}, a_{2}, a_{3},… , The_{no},… }

The_{no} is the generic term of the sequence.

### Examples

1)

2)

If when **no** grow up,** The _{no}** becomes closer and closer to a real number

**L**, the sequence {a

_{no}} has limit L (or converges to L) and writes:

A sequence that is not convergent is called a divergent sequence.

### Sandwich theorem

If {a_{no}}, {B_{no}}, {ç_{no}} are sequences such that_{no} B_{no} ç_{no} for all what if

So

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