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Series and Sequences


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).

The1 = f (1); The2 = f (2); The3 = f (3);…; Theno = f (n)

Notations

{Theno} = {a1, a2, a3,… , Theno,… }

Theno is the generic term of the sequence.

Examples

1)

2)

If when no grow up, Theno becomes closer and closer to a real number L, the sequence {ano} has limit L (or converges to L) and writes:

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

Sandwich theorem

If {ano}, {Bno}, {çno} are sequences such thatno Bno çno for all what if

So

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