This preview shows page 1. Sign up to view the full content.
Unformatted text preview: F 1 = 1, F 2 = 1 deﬁned by the recurrence relation F n = F n1 + F n2 for all n ≥ 2. (a). Write out the ﬁrst 10 terms of this sequence. (b). Use mathematical induction to show that F n = 1 √ 5 " 1 + √ 5 2 ! n1√ 5 2 ! n # . In the base case of this problem, you need to establish that the desired formula holds for n = 0 and n = 1; for the inductive step, you need to assume that F n1 and F n2 can be expressed according to this formula and then conclude that F n can also be expressed according to this formula. [Hint: Compute ± 1+ √ 5 2 ² 2 and ± 1√ 5 2 ² 2 before you start] 1...
View
Full
Document
This note was uploaded on 03/18/2012 for the course MAT MAT 25 taught by Professor Stevenklee during the Fall '10 term at UC Davis.
 Fall '10
 StevenKlee
 Calculus

Click to edit the document details