Quiz 6 - Math XXXXXXXXXX)
Instructions:
• The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score
on the quiz will be converted to a percentage and posted in your assignment folder with
comments.
• This quiz is open book and open notes, and you may take as long as you like on it
provided that you submit the quiz no later than the due date posted in our course
schedule of the syllabus. You may refer to your textbook, notes, and online classroom
materials, but you may not consult anyone.
• You must show all of your work to receive full credit. If a problem does not seem to
equire work, write a sentence or two to justify your answer.
• Please write neatly. Illegible answers will be assumed to be inco
ect.
• Please remember to show ALL of your work on every problem. Read the basic rules fo
showing work below BEFORE you start working on the quiz:
1. Each step should show the complete expression or equation rather than a piece of
it.
2. Each new step should follow logically from the previous step, following rules of
alge
a.
3. Each new step should be beneath the previous step.
4. The equal sign, =, should only connect equal numbers or expressions.
• This quiz is due at 11:59 PM (Eastern Time) on Tuesday, December 6.
***********************
At the end of your quiz you must include the following dated statement with
your name typed in lieu of a signature. Without this signed statement you will
eceive a zero.
I have completed this quiz myself, working independently and not consulting anyone except
the instructor. I have neither given nor received help on this quiz.
Name: Date:
1
Quiz 6 - Sequences & Series
1. Chapter 10-1, Problem 34.
2. Chapter 10-1, Problem 40.
3. Determine whether each of the following series is convergent.
a)
∞∑
k=1
kk
k!
, b)
∞∑
k=1
k!
kk
4. Chapter 10-2, Problem 42.
5. Determine for what values of x the geometric series
∞∑
n=0
πn−1
3n+1 xn
is convergent.
6. Chapter 10-3, Problem 28.
7. Chapter 10-4, Problem 12.
8. Chapter 10-4, Problem 20.
9. Chapter 10-5, Problem 16.
10. Using an appropriate convergence test, determine whether the series
∞∑
n=3
1
n lnn
[
ln(lnn)
]3
is convergent or divergent.
2
103 Geometric and Harmonic S¢ Contemporary Calculus
20. Represent the repeating decimals 0.3 ,0.3b , and 0.abc as geometric series and find the value of
each series as a simple fraction. What do you think the simple fraction representation is for 0.abed ?
In problems XXXXXXXXXXfind all values of x for which each geometric series converges.
21. Zax nk 2 Ie-0k a Ja-w*
& &
K=1
- 3 sink)
i
One student thought the formula was 1+ x+X>4X +... = T—x . The second student said "That
can't be right. If we replace x with 2, then the formula says the sum of the positive numbers
1
XXXXXXXXXXis anegative number T—3 " Who is right? Why?
‘The Classic Board Problem: If you have identical 1 foot long boards, they can be a
anged to hang ove
the edoe of 4 table. One board can extend 172 foot hevond the edoe (Fie 12) two boards can extend