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Introduction to Real sequences; convergent, divergent and oscillating real sequences

First, let's try to understand what sequences really are. So formally, " A sequence in a non-empty set A is a function from  ℕ  into A. " In particular, a real sequence 'a' is a function from  ℕ   into  ℝ .                                                                   i.e., a:  ℕ   →   ℝ . The n th term of the sequence is denoted by a n . Since a sequence is fully described by describing a n  for each n  ∈  ℕ , some of the ways in which we denote a sequence are:  VISUAL REPRESENTATION Imagine a red dot flashing, first at  a 1 , then a 2 and a 3 and so on.  The dots keep on moving until it disappears, i.e., it moves towards infinity for the sequence of natural numbers.  So, the orde...

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