To state : an explicit rule for the
An explicit rule for the
Given information :
The recursively defined sequence
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 :
Consider the recursively defined sequence
And so on.
The sequence is a geometric sequence with
So, the general term is calculated using the formula
Now, to prove that
Conjecture:
Take
Anchor step:
Prove that
For
Inductive hypothesis:
Assume
Inductive Step:
Prove that
Proceed with the sequence formula
Replace
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
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