Exercise 4.1 2. Establish each of the following for all n ≥ 1 by the Principle of Mathematical Induction. Solution a) S(n): ==‚ S(1): = = =1‚ So S(1) is true. Assume S(k): = Consider S(k+1) = = +=-1+= -1. Hence‚ it follows that S(k)⇒S(k + 1) is true for all n ∈ Z+ by the Principle of Mathematical Induction. b) S( n) for n=1‚ = 2 = 2+(1-1). So S(1) is true. Inductive Step: assume S(k)is true‚ for some (particular) k ∈ Z+—that is‚ assume that =2+(k-1). For n=k+1‚ = + (k+1)
Premium Addition Natural number
sure you have 10 pages in your copy of the exam and answer each question in the space provided. You may consult one page of notes and a calculator. I understand that the honor code applies: I will not lie‚ cheat‚ or steal to gain an academic advantage‚ or tolerate those who do. _______________________________________ (Signature) _______________________________________ (Printed Name) _______ (Block) Each of the 11 questions on the exam is worth 10 points. You get 2 points for following
Premium Inflation Central bank Purchasing power parity
IFSM 300 Final Assessment By my signature below‚ I confirm that the work contained here is my own‚ I have received no outside assistance and have properly cited and referenced any external research that has been incorporated in my answers. I have fully complied with UMUC’s Policy on Academic Dishonesty and Plagiarism (Policy 150.25). Failure to properly credit your research sources is a violation of this policy. _____________________________________ (Typed signature represents actual
Premium Management Strategic management Enterprise resource planning
Subject CT3 Probability and Mathematical Statistics Core Technical Time allowed: Three hours INSTRUCTIONS TO THE CANDIDATE 1. Enter all the candidate and examination details as requested on the front of your answer booklet. 2. You must not start writing your answers in the booklet until instructed to do so by the supervisor. 3. Mark allocations are shown in brackets. 4. Attempt all 13 questions‚ beginning your answer to each question on a separate sheet. 5.
Premium Normal distribution
Final Exam Study Guide 1. Which of the following is not a way teams help organizations to succeed? A) Increase information and knowledge B) Increase groupthink among members C) Increase performance levels D) Increase diversity of views 2. A hidden agenda refers to A) a meeting agenda that is not revealed to others outside the meeting group. B) individuals harboring motives that are concealed from the rest of the group. C) an agenda that members must look for before they can attend a meeting. D)
Premium Chart Pie chart Employment
Final Exam A. 8 Elements/ Describe: 1. Be open to group and family approaches- making is a generic term that includes a number of approaches in which family members are brought together to make decisions about how to care for their children and develop a plan for services. Different names used for this type of intervention include family team conferencing‚ family team meetings‚ family group conferencing‚ family team decision-making‚ family unity meetings‚ and team decision-making. 2. Do
Premium School counselor Psychology Psychotherapy
University of Phoenix Final Exam Directions: Based on your readings and discussions in class‚ select the best answer. Utilize the Text Highlight feature or Bold your response. 1. Which of the following types of insurance protects you if you are sued for accidentally damaging someone’s property or hurting another person? a. Term life insurance b. Accidental death insurance c. Universal life insurance d. Personal liability insurance or an umbrella policy 2. To calculate accurately the size
Premium Mutual fund Investment Insurance
instructions Format: The Final Exam consists of a set of 45 questions from 15 important topics presented in the NSA program. You are required to answer only 15 questions from this set. Answers to these questions should be based upon the relevant courses in the program. Each topic contains three skill levels. You need to choose a question which exhibits the highest skill level you can demonstrate fully: Level 1: Definition or basic level. This level shows a basic understanding of the concepts
Premium IP address Internet Internet Protocol
FINAL EXAM: Case Study Alko Inc. Esaam M. Quazi MKTG 3130 Spring 2010 M‚W | 5:45 PM - 7:00 PM Dr. Ram Rachamadugu Consider the case‚ ALKO Inc.‚ described on page 322 and 323 in the text and answer the following questions (do not consider the questions described on page 323). 1. What is the annual inventory and distribution cost of current distribution system? Total Annual Inventory and Distribution Cost | | | | | | | | # of parts | Region 1 | Region 2 | Region 3 | Region
Premium Management Marketing Costs
Math 221 Final exam Review MyStatLab Final Exam Do the Practice Final to help you prepare for the Final Exam. Do the Week 8 Final Exam. Final Exam - Covers All Weeks You must complete this Final Exam. It is designed to test your learning in the course. * Final Exam is worth a total of 250 points and contains 23 questions. * The exam covers all Weeks and all TCOs. * The exam covers Chapters 1-7 and 9 * Remember to submit your exam when you are finished. *
Premium Sample size Statistics Probability theory