To explain how to tell if a geometric series converges or diverges, include examples of both and the evaluate series which converges.
To find if a given geometric series converges or diverges, find the common ratio of the series.
If the absolute value of the common ratio is less than 1, the series converges else diverges.
For example, consider the below two series.
Series 1:
Series:
Common ratio of series 1 is
Now, observe the series 2. Here, the common ratio is
Now, evaluate the series
Use the formula
Here,
Therefore, the sum of the converging series
Chapter 9 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education