MAT 146
Test #4 Part II
Name___________________
50 points (Part II: 30 points)
Calculator Used___________________
Impact on Course Grade: approximately 12.5%
w
Score___________________
n
15. A sequence an is defined as an    .
3
(a) For what values of w will the sequence diverge?

(b) When S   an converges, what is lim an ?
____________
____________
n
n1

16. An infinite series S  bn has a sequence of partial sums, sn, given by
n1
the formula sn 
(a) Is

b
n
3n  5
.
n
2
convergent? If it is, state the sum; if it is not, explain why not.
n1
(b) Calculate
10
b .
n
____________
n1
(c) Determine b1, b2, and b3.
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For questions 17 through 19, determine whether the series converges,
converges absolutely, or diverges. Provide complete and appropriate
justification for your responses.

4
17.  (1)n
n 1
n1
18.

3n
 n  12
n1
19.

2
2
n1 n  3

20. For the power series f (x ) 
following.
(a) the radius of convergence

1n
 n  3n x 1
n
, determine each of the
n1
____________
(b) the interval of convergence
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BONUS!
 2n 
 a . Does
Suppose a sequence is defined recursively with a1 = 2 and an 1  
3n  5 n

 an converge? Provide complete and appropriate justification.
n 1
Calculus II
MAT 146
Test #4
Total Points:
Impact of Exam on Semester Grade:
50
Approximately 12.5%
Evaluation Criteria
Part I: No Calculators
Questions 1 through 10
1 point each with no partial credit. No need to show any work on these.
20 points
Questions 11 and 12
3 points each. Partial credit is possible. Show all steps leading to your solution. Be clear,
complete, and accurate.
Questions 13 and 14
2 points each. Partial credit is possible. Show clear, complete, and accurate sketch for
question 13.
Part II: Calculators Allowed
30 points
State any numerical solutions as exact values in rational expressions reduced to lowest
terms. If approximations are required, express as a decimal value rounded accurately to
the nearest thousandth of a unit.
Questions 15 through 20 are worth 5 points each. Provide appropriate evidence and
clearly stated solutions for each.
15) a) 3 pts b) 2 pts
16) a) 3 pts b) and c) 1 pt each
17) through 19) Show complete and appropriate justification. Be precise and be specific.
20) a) 3 pts b) 2 pts
Bonus!
5 pts: Show complete, accurate, and justified response.