Alternating Series & AS Test Objectives: Be able to describe the convergence of alternating series. Warm Up: Find the sum of the infinite series.

Alternating Series An alternating series is one whose terms alternate in sign. Even terms are neg. Odd terms are neg.

Examples: Write the following alternating series in summation notation

Alternating Series (AS)Test Let an > 0. The Alternating Series and Converge if the following two conditions are met.

Examples: Describe the convergence or divergence of each of the below.

Examples: Describe the convergence or divergence of each of the below.

Examples: Describe the convergence or divergence of each of the below.

Examples: Describe the convergence or divergence of each of the below.

Examples: Describe the convergence or divergence of each of the below.

Absolute Converge If the series converges, then the series also converges. But the converse is not necessarily true. For example

Absolute & Conditional Convergence 1. is absolutely convergent if converges. 2. is conditionally convergent if converges but diverges .

Example: Determine whether or not the series converges or diverges Example: Determine whether or not the series converges or diverges. Classify the convergence as absolute or conditional.

Example: Determine whether or not the series converges or diverges Example: Determine whether or not the series converges or diverges. Classify the convergence as absolute or conditional.

Classify & give as much information as you can for each of the below series.