OSU MTH265 Series - Consider the following series

Question # 00635400
Subject: Mathematics
Due on: 05/23/2022
Posted On: 05/23/2022 03:58 AM
Tutorials: 1
Rating:
4.9/5
Question Dot Image

 

First Name          Last Name           OSU Student ID #

Instructions: Do all of your work on this paper. Scan the completed problems and create one PDF of your work. Your PDF needs to be at least the same number of pages as the original docu- ment. Upload the PDF to this assignment in GRADESCOPE by the due date. (The Gradescope assignment can be accessed through Canvas.)

(1)          Consider the following series.

 ∞           n+1

 S =         (−1)        n

3n

n=1

(a)          Show that the series converges.

(b)          Estimate the error made when the partial sum S10 is used to estimate the series S.

(c)           What is the smallest value of N we could use to estimate the series to within 0.001 ?

 (2)         Consider the following series. For the work that follows, the root or ratio test will likely be convenient!

∞            n

 x

√n

n=1

(a)          Determine the value(s) of x (if any) for which the series converges absolutely.

(b)          Determine the value(s) of x (if any) for which the series converges conditionally.

(c)           Determine the value(s) of x (if any) for which the series diverges.

 (3)         The terms of a series can also be defined recursively. Suppose

1              n + 2

a1 = 4 and an+1 = 3n + 1 an for n ≥ 1

Use an appropriate test to determine whether or not the series converges.

(4)          Generalize the result of the previous exercise. Suppose a1 > 0 and an+1 = f (n)an for some function f . Give a condition on f (n) which would guarantee that such a series converges absolutely.

 (5)         Use either the root or the ratio test on the following series. State your conclusion.

 2+1 • 3 • 4

 3+2 • 4 • 5

 4+3 • 5 • 6

 54 • 6 • 7

 + . . .

 (6)         For the power series below, determine the radius of convergence and interval of convergence. For the interval, be sure to check the endpoints!

n(x − 2)

n=0

 (7)         Use algebraic manipulation of power series to find the first three non-zero terms of the Taylor series for

ex ln(1 + x)

At most partial credit will be awarded for taking derivatives to find this instead of multi- plying the series. The Taylor series for ex and ln(1 + x) are on our posted list of common Taylor series.

Dot Image
dominator0831 Posted By :
Questions: 9146 Tutorials: 9128
Tutorials for this Question

OSU MTH265 Series - Consider the following series

Tutorial # 00634281
Posted On: 05/23/2022 03:58 AM
Feedback Score: Not rated yet!
Purchased By: 2
dominator0831
Posted By:
Questions:
9146
Tutorials:
9128
Report this Tutorial as Inappropriate
Tutorial Preview
The solution of OSU MTH265 Series - Consider the following series...
Attachments
OSU_MTH265_Series_-_Consider_the_following_series.ZIP (18.96 KB)

Great! We have found the solution of this question!

Related Questions
Explain what a confidence interval is, and what is the confidence
Argosy University Probability Worksheet Answering the following including formula references. APA not needed. Explain what a confidence interval is, and what is the confidence level? Explai …
Descriptive Statistics Discussion - When data is collected, the most common
Chamberlain University Descriptive Statistics Discussion Week 1 Discussion: Descriptive Statistics Required Resources Read/review the following resources for this activity: Textbook: Ch …
Statistics - Describe a hypothesis test study that would
Chamberlain University Statistics Questions Required Resources Read/review the following resources for this activity: Textbook: Chapter 9 Lesson Minimum of 1 scholarly source In y …
Colorado MAT122 Week 3 Time and Activity Relation Discussion
Colorado MAT122 Time and Activity Relation Discussion wk 3) Your task for this discussion is as follows: Fill in the table with what you are typically doing during each of the following times. …
Colorado MAT122 Week 2 Time and Activity Relation Discussion
Colorado MAT122 Time and Activity Relation Discussion wk 2) Use an outside source to search for a quadratic equation that models something from your daily life. (Be sure to cite the source you use. …
Colorado MAT122 Week 1 Time and Activity Relation Discussion
MAT 122 Colorado State University Global Campus Time and Activity Relation Discussion wk 1) Research an advertised truck rental price plan that does not include unlimited miles and provide the deta …
GC Working with Radioactive Material Paper
Colorado State University GC Working with Radioactive Material Paper As a scientist, you study 200 grams of a radioactive material for seven months, and suppose you have obtained the following data …
Algebra Polynomial Division Problem Discussion
Colorado State University Algebra Polynomial Division Problem Discussion Write your own polynomial division problem. Solve it using long division and synthetic division. Discuss wh …
Statistics Rstudio Worksheet - The center thickness (in mils)
AU Statistics Rstudio Worksheet ASSIGNMENT E The center thickness (in mils) of a sample of twenty-five contact lenses are given below 0.3978 0.4019 0.4031 0.4044 0.3984 0.3972 0.3981 0.3947 0 …
Exponential Growth in Chessboard Rice Discussion
AU Exponential Growth in Chessboard Rice Discussion Option 2: A person puts an empty chessboard on a table and puts one grain of rice on the first square. Then two grains on the second square, …
Recent Questions
Global Business Etiquette - Imagine you are a communications
Global Business Etiquette Imagine you are a communications specialist for a major corporation that does business across the globe. Your boss is unexpectedly meeting with a potential client from a f …
DEP4305 Discussion - Does being a mother make you an
DEP 4305 Discussion Discussion 1: Does being a mother make you an adult? Scenario: Several years ago, an adult couple gave birth to an infant son who had to be placed in a neonatal intensiv …
Evaluation of counseling sessions - Develop an evaluation tool
INTRODUCTION TO INDIVIDUAL AND GROUP COUNSELING Task 3: Evaluation of counseling sessions Assignment: Develop an evaluation tool to evaluate the effectiveness of group counseling sessions. The t …
Psychology - How do you think that culture and social class affect
Psychology Question How do you think that culture and social class affect gross and fine motor development in early childhood? Provide specific examples. Imagine a parent of a child with deficienci …
SWK516 Earlychildhood Development - How do you think that culture 
swk 516 earlychildhood development How do you think that culture and social class affect gross and fine motor development in early childhood? Provide specific examples. Imagine a parent of a child …
Discussion Part 1,2 - Maintaining relationships
Discussion Part 1 Maintaining relationships In their chapter titled Networking, Hedge and Borman describe multiple strategies for maintaining a business. In this discussion, you will consider …
Assignment 2 - Social Disorganization and Collective Efficacy
Reading Assignment 2 (Section 3) Social Disorganization and Collective Efficacy Introduction, Tammy L. Anderson / Introduction and Growth of Chicago and Differentiation of Loca …
Abstract on Vicarious Trauma - Describe the overall research problem
Abstract on Vicarious Trauma Abstract text must be double-spaced with no paragraph indents or breaks. Describe the overall research problem being addressed in the first couple of sentences and  …
Presidential Controversy - Andrew Jackson’s Presidency is surrounded
Presidential Controversy Andrew Jackson’s Presidency is surrounded with controversy. From increased presidential authority and his battle with the national bank, to the push for a limited gov …
Unit 5 -Provide a statement explain which turning point you
unit 5 checkpoint: turning point topic and explanation provide a statement explain which turning point you will be researching for your final assessment, including why you believe it to be a signif …