To prove: The given statement is true or not for any positive integer using mathematical induction.
Given information:
The given statement is
Formula used :
Follow the steps to prove that the statement is true for any positive integer.
Anchor step: Prove that any statement
Inductive hypothesis: Assume
Inductive Step: Prove that
Explanation:
Conjecture:
Take
Anchor step:
Prove that
For
Inductive hypothesis:
Assume
Inductive Step:
Prove that
This means it is needed to be proved that
Proceed with the inductive hypothesis.
Add
It can be written as:
The statement is same as the statement
So, if
Conclusion:
As
By mathematical induction,
Chapter 9 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
- 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
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