Concept explainers
To prove: The series
Answer to Problem 14P
The proof is given below.
Explanation of Solution
Given:
The given figure is as:
Calculation:
Let length of the base of the first triangle be
By the Pythagorean Theorem, the length of the hypotenuse of the first triangle is
Hypotenuse of the first triangle is the base of the second triangle.
So the base of the second triangle is
Similarly, the base of the third triangle is
Similarly the length of the base of the
The length of the hypotenuse of the
Now using trigonometric ratio in the
Further simplified as:
Now show that series
Consider the series
Use limit comparison test:
Therefore both series are convergent or divergent.
Since using the
Therefore by using the limit comparison test the series
Consider the two series,
If
Therefore, both are convergent or divergent.
But the series
Therefore the series
Hence
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning