Concept explainers
To Find:Explicit formula for
Answer to Problem 26E
Explanation of Solution
Given information:
Use Mathematical induction to prove the above mentioned formula.
Concept used:
1.By using Mathematical induction technique we need to prove that this formula holds True for all natural numbers. The first step is to prove True for
2.Second step by using induction hypothesis of mathematical induction we assume for
3.Third step is we need to prove that above formula is True for
Proof:
From given information
Substitute value of
We get
Similarly
Put
We get
Put
We get
So, we got
Similarly
First, we need to prove the above formula is True for
Given formula is
Put
We get
It True for
Let us assume it is True for
So
We need to prove it is True for
Which is True
So
And hence the proof by Mathematical induction.
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th 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