CSCE 222 CSCE222 Problem Set 6 – Texas A&M
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CSCE 222 CSCE222 Problem Set 6 – Texas A&M
Problem Set 6
Resources.(All people, books, articles, web pages, etc. that have been con-sulted when producing this homework)
Problem 1.(20 pts) Section 5.3, Exercise 6, page 357
Solution..
(a)
f(0) = 1
f(1) =–f(0) =–1
f(2) =–f(1) = 1
f(3) =–f(2) =–1
f(n) = (–1)n
Basis Step:f(0) = 1 = (–1)0
Inductive step:
if f(n)
Description
CSCE 222 CSCE222 Problem Set 6 – Texas A&M
Problem Set 6
Resources.(All people, books, articles, web pages, etc. that have been con-sulted when producing this homework)
Problem 1.(20 pts) Section 5.3, Exercise 6, page 357
Solution..
(a)
f(0) = 1
f(1) =–f(0) =–1
f(2) =–f(1) = 1
f(3) =–f(2) =–1
f(n) = (–1)n
Basis Step:f(0) = 1 = (–1)0
Inductive step:
if f(n) = (–1)n, then
f(n+ 1) =–f(n)
f(n+ 1) =–(–1)n
f(n+ 1) = (–1)n+1
(b) Not a valid recursive definition.
(c) Not a valid recursive definition.
(d)
f(0) = 0
f(1) = 1
f(2) = 2
f(1) = 2
f(3) = 2
f(2) = 4
f(n) = 2n–1
(e)
f(0) = 2
f(1) =f(0) = 2
f(2) = 2f(0) = 4
f(3) =f(2) = 4
f(4) = 2f(2) = 8
f(5) =f(4) = 8
f(6) = 2f(4) = 16
f(n) = 21+bn2c
Problem 2.(20 pts) Section 5.3, Exercise 8, page 358
Solution
CSCE 222 CSCE222 Problem Set 6 – Texas A&M
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