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a) Give a recursive algorithmto solve the following recursive function (hint: use Fibonacci as a reference) _f(0) = 1; f(1) = 2; f(n) = 3 f(n-1) + 4 f(n-2); n > 1. b) Solve f(n) as a function of n (using the method we used in class for Homogenous Equations). Do not solve for the constants.

a) Give a recursive algorithmto solve the following recursive function (hint: use Fibonacci as a reference) _f(0) = 1; f(1) = 2; f(n) = 3 f(n-1) + 4 f(n-2); n > 1. b) Solve f(n) as a function of n (using the method we used in class for Homogenous Equations). Do not solve for the constants.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Problem Description **a) Recursive Algorithm** Give a recursive algorithm to solve the following recursive function (hint: use Fibonacci as a reference). - Initial conditions: - \( f(0) = 1 \) - \( f(1) = 2 \) - Recursive formula: - \( f(n) = 3f(n-1) + 4f(n-2) \); for \( n > 1 \) **b) Solve for \( f(n) \)** Solve \( f(n) \) as a function of \( n \) using the method we used in class for Homogeneous Equations. Do not solve for the constants.
Transcribed Image Text:### Problem Description **a) Recursive Algorithm** Give a recursive algorithm to solve the following recursive function (hint: use Fibonacci as a reference). - Initial conditions: - \( f(0) = 1 \) - \( f(1) = 2 \) - Recursive formula: - \( f(n) = 3f(n-1) + 4f(n-2) \); for \( n > 1 \) **b) Solve for \( f(n) \)** Solve \( f(n) \) as a function of \( n \) using the method we used in class for Homogeneous Equations. Do not solve for the constants.
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