MATH 242: Principles of Analysis
Homework Assignment #7
DUE DATE: Thurs., Nov. 5, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are stro
MATH 242: Principles of Analysis
Homework Assignment #9
DUE DATE: Thurs., Dec. 3, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are stro
MATH 242: Principles of Analysis (Fall 2009)
Practice Problems for the Final Exam
1. Consider the sequence dened recursively by y1 = 1 and yn+1 = 3
1
n N.
yn
(a) Use induction to prove that the sequence cfw_yn is increasing.
(b) Prove that the sequence
MATH 242: Principles of Analysis (Fall 2009)
Practice Problems for Exam 2
1. Construct a divergent sequence that has three convergent subsequences with distinct limits.
2. Construct a bounded sequence that is not Cauchy.
3. Determine whether the given inn
MATH 242: Principles of Analysis (Fall 2009)
Practice Problems for Exam 1
1. Prove that
3
2 is irrational.
2. Use induction to prove that n2 4n for all n 1.
3. Let Pn be the statement that 2 + 6 + 10 + + (4n 2) = 2(n2 + 1).
a) Show that if Pk is true, the
MATH 242: Principles of Analysis
Homework Assignment #8
DUE DATE: Thurs., Nov. 12, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are str
MATH 242: Principles of Analysis
Homework Assignment #6
DUE DATE: Thurs., Oct. 29, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are str
MATH 242: Principles of Analysis
Homework Assignment #5
DUE DATE: Thurs., Oct. 22, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are str
MATH 242: Principles of Analysis
Homework Assignment #4
DUE DATE: Thurs., Oct. 1, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are stro
MATH 242: Principles of Analysis
Homework Assignment #3
DUE DATE: Thurs., Sept. 24, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are st
MATH 242: Principles of Analysis
Homework Assignment #2
DUE DATE: Thurs., Sept. 17, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are st
MATH 242: Principles of Analysis
Homework Assignment #1
DUE DATE: Thurs., Sept. 10, start of class.
Homework should be turned in at the BEGINNING OF CLASS. You should write up solutions
neatly to all problems, making sure to show all your work. You are st