Series - Introduction

Here we introduce the notion of a series of real numbers and look at its important properties. The central question - convergence - is introduced here, but the most important practical results are found in Theory - Testing convergence.

• Introduction: series of real numbers, convergence, reindexing.
• Basic properties: operations, summing over subsets and reordering, convergence.
• Important examples: geometric series, series with powers (p-series).
• Summing up series: geometric, telescopic, Taylor series.
• Approximating series, error of approximation.
• Absolute convergence.