(a) Show that the Maclaurin series of the function f(x) = is E fnx" 1 – x – x? - n=1 where fr is the nth Fibonacci number, that is, fi = 1, f2 for n > 3. [Hint: Write x/(1 - x – x²) = co + c,x + c2x² + · . . and multiply both sides of this equation by 1 – x – x².] (b) By writing f(x) as a sum of partial fractions and thereby obtaining the Maclaurin series in a different way, find an explicit formula for the nth Fibonacci number. 1, and fn = fn-1 + fn-2 = -

(a) Show that the Maclaurin series of the function f(x) = is E fnx" 1 – x – x? - n=1 where fr is the nth Fibonacci number, that is, fi = 1, f2 for n > 3. [Hint: Write x/(1 - x – x²) = co + c,x + c2x² + · . . and multiply both sides of this equation by 1 – x – x².] (b) By writing f(x) as a sum of partial fractions and thereby obtaining the Maclaurin series in a different way, find an explicit formula for the nth Fibonacci number. 1, and fn = fn-1 + fn-2 = -

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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