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 ordering of the flashes determines the order of the sequence. Some cool examples of sequences include the famous Fibonacci sequence, which is usually denoted by F n . Each term of the sequence is the sum o