The Fibonacci sequence is defined formally by setting Fa=0, F =1, and then later terms are...
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The Fibonacci sequence is defined formally by setting Fa=0, F₁ =1, and then later terms are defined by the recursive formula F₁+Fa-F. Vn> 1. (**) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 En|0 1 1 2 3 5 8 l 21 34 55 80 141 23 377 610 Note that what this formule states that if two consecutive terms in the bonaco sequence are added, then the sum equals the next term. For example, if-12, states that F1+Fin - Fint of F₁+Fis= Fix, and this can be seen to be true from the table: 80+144=233 Show that the identity A++++F₁-P₁21 (0) holds for 2-1, 2, 3, 4 by computing each side of (*) separately for those values of a and show that they are equal When - 1 the left sate of (") - F_ and the right side of (") After putting in the values from the tables this states that the left side of (*) - and so both sides are equal When - 2 the left side of (") = P_ F After putting in the values from the tables this states that the left side of (") and the right side of (") and so both sides are equal. +F_ When -3 the left side of (") - P and so both sides are equal. +F_ After putting in the values from the tables, this states that the left side of (") and the right side of(") and the right side of (") +F_ When - 4 the left side of (") - F_ -F_ 1 After putting in the values from the tables, this states that the left side of (") + and so both sides are equal IF_ and the right side of (") and the right side of(") and the night side of (") and the right side of(") The Fibonacci sequence is defined formally by setting Fa=0, F₁ =1, and then later terms are defined by the recursive formula F₁+Fa-F. Vn> 1. (**) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 En|0 1 1 2 3 5 8 l 21 34 55 80 141 23 377 610 Note that what this formule states that if two consecutive terms in the bonaco sequence are added, then the sum equals the next term. For example, if-12, states that F1+Fin - Fint of F₁+Fis= Fix, and this can be seen to be true from the table: 80+144=233 Show that the identity A++++F₁-P₁21 (0) holds for 2-1, 2, 3, 4 by computing each side of (*) separately for those values of a and show that they are equal When - 1 the left sate of (") - F_ and the right side of (") After putting in the values from the tables this states that the left side of (*) - and so both sides are equal When - 2 the left side of (") = P_ F After putting in the values from the tables this states that the left side of (") and the right side of (") and so both sides are equal. +F_ When -3 the left side of (") - P and so both sides are equal. +F_ After putting in the values from the tables, this states that the left side of (") and the right side of(") and the right side of (") +F_ When - 4 the left side of (") - F_ -F_ 1 After putting in the values from the tables, this states that the left side of (") + and so both sides are equal IF_ and the right side of (") and the right side of(") and the night side of (") and the right side of(")
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When n1 the left side of F 1 and the right side of F31 After putting in the values ... View the full answer
Related Book For
Statistical Techniques in Business and Economics
ISBN: 978-1259666360
17th edition
Authors: Douglas A. Lind, William G Marchal
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