(a) Show that the Maclaurin series of the function where f n is the nth Fibonacci number,...
Question:
(a) Show that the Maclaurin series of the function
where fn is the nth Fibonacci number, that is, f1 = 1, f2 = 1, and fn = fn–1 + fn–2 for n ≥ 3. Find the radius of convergence of the series.
(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.
Transcribed Image Text:
f(x) = = X 1 - x - x2 00 is Σ fnx" Μ—|
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a Comparing coefficients of powers of x gives us c 0 0 and In general we have c n c n1 c n2 for n 3 ...View the full answer
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Related Book For
Calculus Early Transcendentals
ISBN: 9781337613927
9th Edition
Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin
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