This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: x and y so that n = 2 x + 5 y . Hint: (2 x + 5 y ) + 2 = 2( x + 1) + 5 y . Reference: [A] An Introduction to Fibonacci Discovery by Brother U. Alfred The Fibonacci Numbers { F n } ∞ n =1 The earliest study of these famous numbers is attributed to Leonardo Of Pisa (alias Fibonacci) early in the thirteenth century. They are associated with a variety of natural phenomena. They are deﬁned recursively by F 1 = 1 F 2 = 1 F n = F n1 + F n2 for n ≥ 3 . So { F n } ∞ n =1 = { 1 , 1 , 2 , 3 , 5 , 8 ,... } Example 3 [A, page 9]: Show that for each n ≥ 2, F 2 nF n1 F n +1 = (1) n1 . Example 4 [A, page 13]: Show that for each n ∈ N F n = 1 √ 5 " 1 + √ 5 2 ! n1√ 5 2 ! n # . Notation suggestion: let r = 1 + √ 5 2 and s = 1√ 5 2 . 2...
View
Full Document
 Fall '10
 Girardi
 Integers, Natural Numbers, Mathematical Induction, Natural number, Peano axioms, inductive step, Brother U. Alfred

Click to edit the document details