Concept explainers
To proof: The expression
Explanation of Solution
Given information:
The expression
Formula used:
The steps to prove a statement by mathematical induction are as follows:
Step 1. Show that the statement is true for
Step 2. Assume that the statement is true for
Step 3. Prove that the statement is true for
Proof:
Consider expression
Denote the expression by
Recall that the steps to prove a statement by mathematical induction are as follows:
Step 1. Show that the statement is true for
Step 2. Assume that the statement is true for
Step 3. Prove that the statement is true for
Substitute
The above equation holds true.
Therefore, the statement is true for
Now, assume that the statement if true for
Therefore, the statement holds true for
Now, prove it for
Substitute the value of
Result obtained is that
Hence, by the principle of mathematical induction the statement
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