Description

We conclude this subject with the notion of natural patterns. To this end, we investigate sequences, series, and summation notation; arithmetic and geometric sequences and series; and the Binomial Theorem.

Sections of this topic include:

1. Sequences, Series, and Summation Notation

   In exploring this topic, we begin by investigating sequences, series and the summation notation. Groups within this section include: finding the first five terms of a sequence; finding the general term of a sequence; evaluating a series; writing a series in sigma notation; finding the first six terms given a recursive sequence.

2. Arithmetic Sequences and Series

   With an understanding of what sequences and series are, we now focus on arithmetic sequences and series. Groups within this section include: determining if a sequence is arithmetic and finding a common difference; and finding the sum of an arithmetic series.

3. Geometric Sequences and Series

   Continuing our investigation of sequences and series, we discover geometric sequences and series. Groups wthin this section include: determining if a sequence is geometric and finding a common ratio; finding the sum of a geometric series; evaluating infinte geometric series; writing a decimal number as a rational number.

4. The Binomial Theorem

   We conclude this topic with the Binomial Theorem which allows us to expand binomials to powers. Groups within this section include: evaluating factorials and combinations; writing quantities as the quotient of two factorials; using the Binomial Theorem to expand powers; and finding terms of a Binomial Expansion.