Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter30: Customary And Metric Steel Rules
Section: Chapter Questions
Problem 18A
Related questions
Topic Video
Question
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
Expert Solution
Step 1
The general form of the geometric series is given by:
where is said to be the first term and r is the common ratio.
This series is divergent if and convergent if .
And, the sum of this series is given as (if it is convergent) :
Step 2
The given series is :
For, this series, the first term is , and the common ratio is
Since the absolute value of the common ratio is , which is less than 1, that is .
Therefore, the given series is convergent.
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning