MATH10550 Midterm: MATH 10550 Exam 3 Spring 2012
Name:
Instructor:
Math 10560, Practice Exam 3
April 18, 2012
•The Honor Code is in effect for this examination. All work is to be your own.
•No calculators.
•The exam lasts for 1 hour and 15 min.
•Be sure that your name is on every page in case pages become detached.
•Be sure that you have all 9 pages of the test.
PLEASE MARK YOUR ANSWERS WITH AN X, not a circle!
1. (a) (b) (c) (d) (e)
2. (a) (b) (c) (d) (e)
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3. (a) (b) (c) (d) (e)
4. (a) (b) (c) (d) (e)
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5. (a) (b) (c) (d) (e)
6. (a) (b) (c) (d) (e)
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7. (a) (b) (c) (d) (e)
8. (a) (b) (c) (d) (e)
Please do NOT write in this box.
Multiple Choice
9.
10.
11.
12.
Total
Name:
Instructor:
Multiple Choice
1.(7 pts.) Find
∞
X
n=1
22n
3·5n−1.
(a) 4
15 (b) 5
4(c) 5
12 (d) 5
3(e) 20
3
2.(7 pts.) The series
∞
X
n=2
(−1)n+1
√n
(a) diverges even though lim
n→∞
(−1)n+1
√n= 0.
(b) does not converge absolutely but does converge conditionally.
(c) diverges because lim
n→∞
(−1)n+1
√n6= 0.
(d) converges absolutely.
(e) diverges because the terms alternate.
2
Name:
Instructor:
3.(7 pts.) Use Comparison Tests to determine which one of the following series is diver-
gent.
(a)
∞
X
n=1
1
n3
2+ 1
(b)
∞
X
n=1
1
n2+ 8 (c)
∞
X
n=1
n2−1
n3+ 100
(d)
∞
X
n=1
n
n+ 11
2n
(e)
∞
X
n=1
75
6n
4.(7 pts.) Consider the following series
(I)
∞
X
n=1 2n2+ 7
n2+ 1 n(II)
∞
X
n=2
21/n
n−1(III)
∞
X
n=1
n!
en
Which of the following statements is true?
(a) (I) converges, (II) diverges, and (III) converges.
(b) (I) diverges, (II) diverges, and (III) converges.
(c) (I) converges, (II) diverges, and (III) diverges.
(d) They all diverge.
(e) They all converge.
3
Document Summary
2. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) 4. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) 6. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) 8. (a) (a) (b) (b) (c) (c) (d) (d) (e) (e) The series (a) diverges even though lim n . = 0. (b) does not converge absolutely but does converge conditionally. (c) diverges because lim n ( 1)n+1. 6= 0. (d) converges absolutely. (e) diverges because the terms alternate. Use comparison tests to determine which one of the following series is diver- gent. (a) (d) Xn=1 (cid:16) 2n2 + 7 n2 + 1 (cid:17)n (ii) Which of the following statements is true? (a) (i) converges, (ii) diverges, and (iii) converges. (b) (i) diverges, (ii) diverges, and (iii) converges. (c) (i) converges, (ii) diverges, and (iii) diverges. (d) they all diverge. (e) they all converge.
