THE UNIVERSITY OF MANITOBA
March 11, 2011
DEPARTMENT & COURSE NO: Mathematics 2730
EXAMINATION: Sequences and Series TIME: 1 HOUR
LASTNAME(FamilyName):(Printinink)
FIRSTNAME(GivenName):(Printinink)
ST
UNIVERSITY OF MANITOBA
DATE: March 12, 2014
MIDTERM 2
PAGE: 1 of 5
TIME: 75 minutes
EXAMINER: Harland
DEPARTMENT & COURSE NO: MATH 2730
EXAMINATION: Sequences and Series
1. For the series:
n=1
(1)n+1
MATH 2730 Assignment 1
Solutions
1
=0.
n ln(n + 1)
Solution. We need to show that for every > 0 , there is a number M, such that for every
1
n > M , we have
0 < . We consider the last inequality firs
136.271 Assignment 2
Solutions
Note before you start: there are many ways to solve the problems below, and I do
not claim the solutions below are the shortest. They are just the first to come.
1. Use
MATH 2730 Assignment 3
Due March 10, 2008, (Solutions)
1. Which of the following series converges absolutely, which converges conditionally
and which diverges? Justify your answers.
(1) n +1 (0.1) n
n
MATH 2730 Sequences and Series
Midterm Exam
5:30-6:30, February 27, 2008
Brief Solutions
1.
(a) Complete the following definition: A sequence cfw_an =1 converges to a number L
n
(written lim an = L )
1. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.
Justify your answer.
(a)
n=1
(b)
n=1
(c)
n=3
(d)
n
(1)n 5+n
sin(4n)
2n
[8]
[8]
(1)n ln n
n
[8]
an wher
FINAL EXAM OF DEC. 2009
(1) Determine whether the series is absolutely convergent, conditionally convergent, or
divergent. Justify your answer.
(a)
(b)
(c)
n=1
n=2
n=1
1
(n + 1) 2 ( 1 )n+1
2
(1)n
n
1
THE UNIVERSITY OF MANITOBA
February 7, 2011
DEPARTMENT & COURSE NO: Mathematics 2730
EXAMINATION: Sequences and Series TIME: 1 HOUR
TERM TEST 1
PAGE NO: 1 of 11
EXAMINER: Kalajdzievski
Values
[8] 1. (
UNIVERSITY OF MANITOBA
DATE: February 6, 2014
MIDTERM 1
PAGE: 1 of 7
TIME: 75 minutes
EXAMINER: Harland
DEPARTMENT & COURSE NO: MATH 2730
EXAMINATION: Sequences and Series
[6] 1. Find the limit of the
Winter 2008 Final (Warning: This test was only 2 hours long, not 3. Hence its not
indicative of the length)
1. Determine if the sequence cfw_an converges of diverges. In the case it converges, nd the
Math 2730 Assignment 4
Solutions
1. Find the power series with sum equal to g(x) =
x2
and find the interval of
(1+ 2x) 2
convergence of the power series.
Solution. First we focus on the function h(x)