Take-Home Quiz # 6

(Sections 10.1 – 10.5)

Math 141/7381, Due 11:59PM, Tuesday, December 6, 2022

Instructions: This quiz must be completed independently. You are allowed to consult with your notes or the eBook as needed to aid you in solving these problems. Seeking help from others in or out of the class is not allowed.

Suggestions about how to approach this quiz:

1. Finish all homework assignments of the sections and get good understanding of the contents from the last week.

2. Print out a copy of the quiz and solve any problems that you can, using pencil and paper.

3. Review the eBook sections associated with any problems you could not solve.

4. Complete the remaining problems to the best of your ability. Even if you cannot come to a final solution, you should show what you do know so that you have the opportunity for partial credit.

5. Review your work. Check for errors. Make sure you have included units where appropriate, and explanations when required by the instructions.

6. When you are satisfied, type in your solutions ( extend space if needed ), or scan your hand written work, or insert photo images into one document. Make sure that your submission is readable.

7. Submit your work in the associated LEO assignment.

Unless the problem explicitly states otherwise, work must be shown for every answer. Any answer, even if “correct” but lacking work, will NOT receive full credit and may receive NO credit!

Please submit the quiz as an attachment in any readable formats such as scanned or photo copy before or on Tuesday, December 6. No late quiz will be accepted. No make-up quiz will be arranged. A solution key for Quiz # 6 will be posted along with the quiz right after the deadline.

Please sign (or type) your name below the following honor pledge:

I have completed this quiz by myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz.

Name _____________________Date___________________

QUIZ # 6 Problems

1. Calculate the first 10 terms (starting with ) of the sequence

2. State whether the sequence converges or diverges? If the sequence converges, find its limit .

3. Does the series definitely diverge by the nth Term Test ? If not, what can we conclude?

4. Rewrite the geometric series using the sigma notation and calculate the value of the sum.

5. Find all values of x for which the geometric series converges and find its sum.

6. Calculate the value of the partial sum for and , find a formula for general partial sum Sn, and then find the limit of as n approaches infinity.

7. Use the Integral Test to determine whether the following series converges or diverges. Solving using other methods will not be credited.

(a) (b)

8. Use the Comparison Test or the Limit Comparison Test to determine whether the given series converges or diverges. Solving using other methods will not be credited.

(a) (b) (Hints: )