(a)
To Show: The MacLaurin series of the function
(a)
Explanation of Solution
Given:
The
Calculation:
The given function is,
Then write the function as,
Multiply both the sides of the equation by
Then, expand the above equation and factorize as,
Then, compare the coefficient and the power of
Solve further as,
Thus, the required sequence is,
Thus, for
Hence, proved.
(b)
To Find: The writing
(b)
Answer to Problem 16P
The explicit formula for the nth Fibonacci number is
Explanation of Solution
Calculation:
The given function is,
Factorize the denominator as,
Then, by the partial decomposition,
Solve further as,
Solve for B as,
Thus, the required expression as,
Then, solve the equation as,
Then, from part (a),
Thus, the explicit formula for the nth Fibonacci number is
Chapter 8 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning