Sequences & Series

• Covers: This comprehensive module delves into the fundamental concepts of sequences and series. It begins with arithmetic sequences and series, including recursive definitions, sigma notation, and the arithmetic sum formula. It then progresses to geometric sequences and series, covering their classification, sum formulas for n terms, and the concept of infinite sum series. The module concludes with an in-depth exploration of infinite series, discussing methods like the differences method, various convergence tests (direct, limit comparison, integral), conditional and absolute convergence, convergence intervals of power series, and the approximation of infinite series, culminating in Taylor and Maclaurin series.

• Outcomes:  Identify, define, and calculate terms and sums of arithmetic sequences and series, including using sigma notation.  Recognize, classify, and apply formulas for geometric sequences and series, including infinite sums.  Determine the convergence or divergence of various infinite series using multiple test methods.  Understand and apply concepts of conditional and absolute convergence.  Work with convergence intervals of power series.  Approximate infinite series and construct Taylor and Maclaurin series.