BSED Program

Palawan State University

Palawan College of Arts and Trades

Midterm Examination in Math 17

Calculus III
Second Semester, A.Y. 2024-2025

General Instruction:
a. This test is worth 50 points. The topics covered in this test are I-Sequences and Infinite Series; II-Power series.
b. Print this test questionnaire on an A4 size paper and answer.
c. Write your explanation/solution in the boxes provided after the item. Show the necessary steps.
d. Answers to the multiple-choice questions should be written on the answer sheet found on the last page of this
test questionnaire. Solutions will have corresponding points.
e. Submit your papers on or before April 14, 2025 (Monday).

I. MULTIPLE CHOICE WITH FREE RESPONSE. Read each question carefully. Shade the letter that correspond
to your answer on the provided answer sheet. Show your steps in the boxes provided after the item.
1. (1 point) Which of the following consists of the elements of a sequence function listed in order?
A. Sequence B. Geometric sequence C. Series D. Geometric series
2. (1 point) Which of the following denotes an infinite series?
A. {an }
B. {1, 2, 3, ..., n, ...}
+∞
X
C. un = u1 + u2 + u3 + ... + un
n=1
+∞
X
D. un = u1 + u2 + u3 + ... + un + ...
n=1

3. (1 point) Which of the following best describes an infinite series?

A. The product of the terms of an infinite sequence.
B. The limit of the partial sums of the terms of an infinite sequence.
C. A list of numbers arranged in a particular order that goes on forever.
D. A function that repeats its values at regular intervals over an infinite domain.
4. (3 points) Is the sequence given below increasing, decreasing, or not monotonic?
 
3n − 1
4n + 5
A. Increasing B. Decreasing C. Not monotonic D. Can’t tell

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5. (3 points) Is the sequence given below increasing, decreasing, or not monotonic?
 
2n − 1
4n − 1
A. Increasing B. Decreasing C. Not monotonic D. Can’t tell

6. (3 points) Is the sequence given below increasing, decreasing, or not monotonic?

nno
2n
A. Increasing B. Decreasing C. Not monotonic D. Can’t tell

n2 + 3
 
7. (3 points) Is the sequence bounded or not bounded?
n+1
A. Bounded B. Not bounded C. Can’t tell

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n 1 2 3 4 n
8. (3 points) Is the sequence whose elements are , , , , ..., , ... bounded?
2n + 1 3 5 7 9 2n + 1
A. Bounded B. Not bounded C. Can’t tell

9. (3 points) Is the sequence {n} whose elements are 1, 2, 3, 4, ..., n, ... bounded?
A. Bounded B. Not bounded C. Can’t tell

+∞
X
10. (2 points) Determine if the infinite series n is convergent or divergent. If it is convergent, find its sum.
n=1
1
A. 2 B. 1 C. 2 D. divergent

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 n2
 
11. (3 points) Given the sequence of the partial sums of the series {sn } = , determine whether the infinite series
n+1
is convergent or divergent. If it is convergent, find its sum.
1
A. 2 B. 0 C. 1 D. divergent

+∞
X 2
12. (3 points) Determine if the infinite series n−1
is convergent or divergent. If it is convergent, find its sum.
n=1
3
A. 1 B. 2 C. 3 D. divergent

13. (4 points) Determine the interval of convergence of the following power series.

+∞ n n
X 2 x
n=1
n2

A. −1 < x < 1 B. − 12 < x < 1

2 C. −2 < x < 2 D. − 13 < x < 1
3

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14. (4 points) Determine the interval of convergence of the following power series.

+∞
X nxn
n=1
3n

A. −2 < x < 2 B. − 12 < x < 1

2 C. −3 < x < 3 D. − 13 < x < 1
3

15. (5 points) Determine the interval of convergence of the following power series.

+∞
X (x + 2)n
n=1
(n + 1)2n

A. −2 < x < 2 B. −3 < x < 1 C. 0 < x < 4 D. −4 < x < 0

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16. (5 points) Determine the interval of convergence of the following power series.

+∞ 2
X n
(x − 1)n
n=1
5n

A. −4 < x < 6 B. 0 < x < 4 C. 2 < x < 8 D. −3 < x < 7

17. (1 point) Find the radius of conver-

gence of the series Last Name, First Name M.I.
+∞ 3 n
X n x

20-MCQ-with-ZipGradeID (6958)
3n Quiz
ExamName
Name Course, Yr. & Sec.
n=1
ZipGrade.com

1
A. 0 B. 3 C. 1 D. 3
18. (1 point) Find the radius of conver-
gence of the series 1 A B C D E 16 A B C D E

+∞ 2 A B C D E 17 A B C D E
X nxn
3n 3 A B C D E 18 A B C D E
n=1

A. 1
B. 1
C. 2 D. 3 4 A B C D E 19 A B C D E
2 3
19. (1 point) Find the radius of conver- 5 A B C D E 20 A B C D E

gence of the series 6 A B C D E

Student ID
+∞
X n 2 7 A B C D E
(x − 1)n
n=1
5n 0 0 0 0 0

A. 2 B. 3 C. 4 D. 5 8 A B C D E 1 1 1 1 1

2 2 2 2 2
9 A B C D E

3 3 3 3 3
10 A B C D E
4 4 4 4 4
11 A B C D E
5 5 5 5 5
12 A B C D E
6 6 6 6 6
13 A B C D E
7 7 7 7 7

14 A B C D E
8 8 8 8 8

15 A B C D E 9 9 9 9 9

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