Series

Author: John J Weber III, PhD Corresponding Textbook Sections:

• Section 11.2 – Series

Expected Educational Results

• Objective 19–01: I can explain the difference between a series and a sequence.

• Objective 19–02: I can classify a series as geometric, $p$$p$-series, harmonic, or telescoping.

• Objective 19–03: I can explain what it means for a series to converge and diverge.

• Objective 19–04: I can explain why ${\displaystyle \underset{n\to \mathrm{\infty }}{lim}{a}_n=0}$$\displaystyle\lim_{n\rightarrow\infty}{a_n}=0$ is a necessary but not sufficient condition for series convergence.

• Objective 19–05: I can use the appropriate Series Convergence Test to determine if a series converges or diverges.

• Objective 19–06: I can compute the interval on which a power series converges.

• Objective 19–07: I can compute the sum of a convergent geometric series.

• Objective 19–08: I can compute the sum of a telescoping series.

• Objective 19–09: I can use a geometric series to rewrite a repeating decimal as a rational number.

Bloom’s Taxonomy

A modern version of Bloom’s Taxonomy is included here to recognize various different levels of understanding and to encourage you to work towards higher-order understanding (those at the top of the pyramid). All Objectives, Investigations, Activities, etc. are color-coded with the level of understanding.

Series

Activity 01

The pattern of the triangles that you see in the figure above continues infinitely.

1. Identify the fraction represented by each triangle. Explain.

2. Find the total sum of all fractions. Explain.

Activity 02

The pattern of the purple shaded region that you see in the figure above continues infinitely.

1. Identify the total sum of the region shaded in purple. Explain.

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Last Modified: Thursday, 12 November 2020 6:42 EDT