Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
(d) Let v := (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...) be the usual sequence of Fibonacci numbers, in which each integer in the sequence is the sum of the previous two. Express v as a linear combination of the vectors (@")n>o and (B")n>0, and use this to obtain a closed formula for the nth Fibonacci number, i.e., the n-th term in the sequence v.

(d) Let v := (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...) be the usual sequence of Fibonacci numbers, in which each integer in the sequence is the sum of the previous two. Express v as a linear combination of the vectors (@")n>o and (B")n>0, and use this to obtain a closed formula for the nth Fibonacci number, i.e., the n-th term in the sequence v.

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
See similar textbooks
icon
Related questions
Question

*I only need part d)

(c) Let o := 1+v5 be the golden ratio, and let ß := 1-V5 Ey. Show that the sequences (@")n20 and (ß")n20 form a basis for W. (d) Let v := (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...) be the usual sequence of Fibonacci numbers, in which each integer in the sequence is the sum of the previous two. Express v as a linear combination of the vectors (@")n20 and (B")n>0, and use this to obtain a closed formula for the nth Fibonacci number, i.e., the n-th term in the sequence v.
Transcribed Image Text:(c) Let o := 1+v5 be the golden ratio, and let ß := 1-V5 Ey. Show that the sequences (@")n20 and (ß")n20 form a basis for W. (d) Let v := (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...) be the usual sequence of Fibonacci numbers, in which each integer in the sequence is the sum of the previous two. Express v as a linear combination of the vectors (@")n20 and (B")n>0, and use this to obtain a closed formula for the nth Fibonacci number, i.e., the n-th term in the sequence v.
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS