To prove the inequality
Answer to Problem 30E
The inequality
Explanation of Solution
Given:
Let
Concept used:
The Principle of Mathematical Induction states that for a statement
1.
2. for every positive integer k , the truth of
Calculation:
First to show that the property is valid for
Now, let us assume that for
we need to show that for
For
From (1) and the assumption taken we know,
Hence, proved.
Therefore, by combining all the results, we can conclude by the mathematical induction that the inequality is valid for all
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
- 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