Math 327A Exercises 4. Due Wednesday, February 3, 2010.
Problems from the book, chapter 16.
Deﬁnition: Consider some set S of real numbers. A real number a is an accumulation point
of the set S if for each positive value ǫ, there is a number xǫ in S (othe

Math 327A Exercises 4. Due Wednesday, Feb 3, 2010.
Problems from the book, chapter 16.
Deﬁnition: Consider some set S of real numbers. A real number a is an accumulation point
of the set S if for each positive value ǫ, there is a number xǫ in S (other tha

Math 327A. Exercise 3, due Wednesday, January 27, 2010.
An increasing sequence {an }∞ converges if and only if the set of terms of the sequence
n=1
has an upper bound. If the set of terms of the sequence has an upper bound, the sequence
converges to the l

Math 327A. Exercise 3, due Wednesday, January 27, 2010.
An increasing sequence {an }∞ converges if and only if the set of terms of the sequence
n=1
has an upper bound. If the set of terms of the sequence has an upper bound, the sequence
converges to the l

Math 327A Exercise 2. Due Wednesday, January 20, 2010.
1
1. The decreasing sequence { n }∞ converges to 0. What can you say about the sequence
n=1
{1/3, 1/2, 1, 1/6, 1/5, 1/4, 1/9, 1/8, 1/7, .}?
Solution: The sequence is not decreasing, but its limit is s

Math 327A Exercise 2. Due Wednesday, January 20, 2010.
1
1. The decreasing sequence { n }∞ , i.e., the decreasing sequence 1,1/2.1/3,1/4,1/5,1/6,.,1/n,.
n=1
converges to 0. The sequence {1/3, 1/2, 1, 1/6, 1/5, 1/4, 1/9, 1/8, 1/7, .} is not decreasing,
but

Math 327A Exercise 1. Due Monday, January 11, 2010.
From the beginning, it should be understood that limt→∞
t ranges over the positive integers.
1
t
= 0. In that equality, the variable
Let {an }∞ be an inﬁnite sequence of real numbers, and let m be a real

Math 327A Exercise 1. Due Monday, January 11, 2010.
From the beginning, it should be understood that limt→∞
t ranges over the positive integers.
1
t
= 0. In that equality, the variable
Let {an }∞ be an inﬁnite sequence of real numbers, and let m be a real

Math 327A. Sample midterm problems. February 5, 2010.
1
1. Check that the series Σ∞ n ln2 n converges and give the best upper bound on its value
n=2
that you can.
2. The ratio test is disappointing for Σ∞ an when limn→∞ an+1 = 1, because it gives
n=0
an

MATH 327 Winter 2010
Instructor: John Sullivan
Oﬃce: Padelford C-341. Phone 543-7986.
E-mail: sullivan@math.washington.edu
Oﬃce hours: M 1:45-2:45, Tu 1:30-2:30 or by appt.
Web page: www.math.washington.edu/ sullivan/personal.html
Text: Advanced Calculus,