Sequences and Series
A loan that grows by the same percentage each year, a ball that bounces back to two-thirds of its height, a pattern of tiles that adds three more each row: these are sequences, and adding their terms gives a series. In this chapter you revisit arithmetic progressions, meet geometric progressions and their sums, and prove that the arithmetic mean is never less than the geometric mean. Python lists terms and partial sums so you can check every formula.
Part of Mathematics · High School (11–12) (chapter 5)
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Sequences, Series and Arithmetic Progressions
Sequences given by a formula or a rule, series and sigma notation, then arithmetic progressions in depth: the nth term, the sum, properties, and the arithmetic mean.
Geometric Progressions and the AM-GM Inequality
Geometric progressions: the nth term, the sum of n terms and the sum to infinity, the geometric mean, and the relation between the arithmetic and geometric means.