Introduction to Sequences

Here we introduce the basic notion of a sequence, cover the most important examples and look at some basic properties.

• Introduction: Definition, sequences given by a formula, recursive definition; subsequence.
• Basic properties: Boundedness, monotonicity.
• Important examples: alternating, arithmetic and geometric sequence, 1/n.
• Operations with sequences.

For the explanation of the relationship between sequences and functions (which is also relevant to the boundedness and monotonicity), see Sequences and functions in Theory - Limits.