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APPM 1360
EXAM #3
FALL 2007
On the front of your bluebook, please write: a grading key, your name, student ID, and
section and instructor (Dougherty, section 10, or Li, section 30 with lecture at 1 pm or
section 20 with lecture at 2 pm).
This exam is worth 100 points and has 5 questions.
Show all
work!
Answers with no justiﬁcation will receive no points.
1. (20 points) A few unrelated questions. Justify your answer in each case.
(a) Does
∞
X
n
=1
1
1 + 2 + 3 +
· · ·
+
n
converge or diverge?
(b) Does
∞
X
n
=1
(

1)
n
n
converge or diverge?
(c) Find the limit: lim
x
→
0
sin
x

x
+ (
x
3
/
6)
x
5
.
2. (30 points) Consider the series given by
∞
X
n
=2
x
n
n
ln
n
Justify each answer carefully and completely.
(a) What is the radius of convergence for this series?
(b) For what values of
x
does the power series converge absolutely?
(c) For what values of
x
does the power series converge conditionally (but not absolutely)?
(d) For what values of
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 Winter '06
 LIM,JISUN

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