This preview shows page 1. Sign up to view the full content.
Unformatted text preview: n is a natural number, and n ≥ 11. To save time, you may use the fact that: n 3 = ( n1) 3 + 3 n 23 n + 1 . 5. (2 points) Let F n be the Fibonacci sequence, given recursively by the following: • F = 1, and F 1 = 1. • If n ∈ N , and n ≥ 2, then F n = F n1 + F n2 . Prove that if n ∈ N , and if F n is even, then F n +1 is odd. 6. (3 points) Let S be the set of ordered triples ( x,y,z ), such that x,y,z ∈ Z , x > 0, y > 0, z > 0, and x + y + z = 100. For example, (1 , 9 , 90) ∈ S , and (40 , 40 , 20) ∈ S . How many elements does S have?...
View
Full
Document
This test prep was uploaded on 04/17/2008 for the course MATH 100 taught by Professor Weissman during the Fall '08 term at University of California, Santa Cruz.
 Fall '08
 Weissman
 Math

Click to edit the document details