Math 21C  Sec 002
Midterm Exam
July 12, 2007
Name
..........................................
Student ID Number
............................
Math 21C Midterm  Summer Session 1
Instructor: Stephen Ng
Instructions:
1. You have 1 hour to complete this exam. Budget your time wisely.
2. The exam is to be closed book and closed notes, except for an approved 8.5
×
11 handwritten sheet.
3. No calculators are allowed.
4. Show all work. Answers without proper justification will receive no credit.
5. Do not write things that you know to be false. Partial credit will be given for proper application of
inconclusive tests.
6. Negative points will be rewarded for committing the ultimate sin! Remember that the
n
th term test
can only be used for divergence.
Question
Points
Score
1
20
2
20
3
20
4
20
5
20
6
20
Total:
120
Math 21C  Sec 002
Midterm Exam
July 12, 2007
1. (20 points) The Taylor series for ln(1 +
x
) is
∞
n
=1
(

1)
n

1
x
n
n
=
x

x
2
2
+
x
3
3
 · · ·
+ (

1)
n

1
x
n
n
+
· · ·
(a) Find the radius of convergence and the interval of convergence. For which points is the convergence
absolute? For which points is the convergence conditional?