Discrete Mathematics教学习题（华南理工）Tutorial06-Answer.pdfVIP

Discrete Mathematics I (Semester 2, 2013-2014) Tutorial 06 - Answer Refer to Chapter 2.4 Date: April-2014 1. List the first 5 terms of each of these sequences. a) the sequence that begins with 2 and in which each successive term is 3 more than the preceding term b) the sequence that begins with 3, where each succeeding term is twice the preceding term c) the sequence where the nth term is the number of letters in the English word for the index n Answer: a) {2, 5, 8, 11, 14…}. b) {3, 6, 12, 24, 48…} c) {a, b, c, d, e…} Discrete Mathematics I – Tutorial 6 1 2. For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence. a) 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, ... b) 15, 8, 1, -6, -13, -20, -27,... c) 3, 5, 8, 12, 17, 23, 30, 38, 47, ... d) 2, 16, 54, 128, 250, 432, 686, ... Answer: a) {k ones and k zeros} k=1, 2… n. 1, 1, 1 b) an = 22-7n -34, -41, -48 2 c) a = 3+2+3+4+5+…= (n +n+4)/2 n 57, 68, 80 d) an = 2n3 1024, 1458, 2000 Discrete Mathematics I – Tutorial 6 2 3. Assume S = {1, 3, 5, 7}, What are the values of these sums? f) ∑j 2 g) ∑1 j S∈ j S∈ Answer: f) ∑j 2 = 1+