MAST20026 Real Analysis Semester 2, 2020 Assignment 3 Due: Wednesday, 16th September (11:59pm) Write your name and your student number in the spaces provided below. Late assignments will be accepted with a 25% reduction for each day late. Full working must be shown in your answers. Assignments should be neatly handwritten in blue or black pen. To complete this assignment you should write your solutions into the blank answer spaces following each question. – If you have a printer (or can access one), then you should print out the assignment template, handwrite your solutions into the answer spaces and then scan your assignment to a PDF file for upload; If you do not have a printer, but you can annotate a PDF using an iPad/Android tablet/Graphics tablet, then annotate your answers directly onto the assignment PDF and save a copy for submission; – Whether you complete on paper or by annotating the pdf, if you find you are unable to answer the whole question in the answer space provided then you can append additional handwritten solutions to the end of your template assignment. If you do this you must make a note in the correct answer space for the question, warning the marker that you have appended additional remarks at the end. When complete, scan your assignment and upload in ‘GradeScope’. Students must not seek or obtain help with assignment questions from others, including: fellow students, University employees or people from outside the University, whether in person or via social media (or other means of communication). Seeking, obtaining or providing such help is considered to be academic misconduct. Posting assignment questions on internet sites is strictly forbidden. Name: Student ID: The assignment begins on the next page. Mathematics and Statistics 1 of 3 University of Melbourne MAST20026 Real Analysis Semester 2, 2020 1. Use Mathematical Induction to prove that for all positive integers n n∑ j=1 (−1)j(j − 1) · j = 1 · 2− 2 · 3 + ... + (−1)n(n− 1) · n = { n2 2 n even 1−n2 2 n odd . Mathematics and Statistics 2 of 3 University of Melbourne MAST20026 Real Analysis Semester 2, 2020 2. Define S = {x ∈ R | ∃y > 0, x = y + 1y}. In the following proofs, clearly state the axioms for R or theorems used. (a) Prove that S is not bounded above. (b) Prove that S is bounded below. (c) Guess the infimum inf S and prove that your guess is correct. Mathematics and Statistics 3 of 3 University of Melbourne
欢迎咨询51作业君