About MTH621 Assignment 1
MTH621 Assignment No 1 for Fall 2026 is from Real Analysis I. It covers lesson 48: Theorem On Algebra Of Limits, carries 20 marks and is due on VULMS by 11:59 pm on Friday 13 November 2026. You can request the solution from this page.
- Course
- MTH621 Real Analysis I
- Assignment
- Assignment No 1
- Semester
- Fall 2026
- Lesson
- 48: Theorem On Algebra Of Limits
- Total marks
- 20
- End date
- Fri 13 Nov, 11:59 pm
What MTH621 Assignment 1 asks
This assignment covers fundamental concepts from the first eleven lectures of the course, specifically focusing on sequences and sets in real analysis. Students are required to solve four mathematical problems involving limits, convergence, and set properties. You must show all necessary steps and explicitly state any formulas or theorems applied to reach your conclusions.
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1
Problem 1
Calculate the limit of the sequence defined by sn = 1/n + 2(1 + 3/n) / (1 + 1/n). Ensure all algebraic steps are clearly documented.
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2
Problem 2
Provide a formal proof demonstrating that if a sequence {sn} is non-decreasing, then its limit as n approaches infinity is equal to the supremum of the set {sn}.
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3
Problem 3
Analyze the sequence {(2n+1)/n} to determine whether it converges or diverges. Provide a logical discussion to support your conclusion.
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4
Problem 4
Identify an open cover for the set A = {0, 1, 1/2, 1/3, ..., 1/n, ...} within the set of real numbers R.
- What to submit
- One MS Word file uploaded to the LMS.
- Topics covered
- Sequence limits Monotone sequences Supremum Convergence and divergence Open covers Real analysis
A summary of the assignment file, Fall 2026_MTH621_1.pdf. Download the file for the full wording before you start.
Lesson covered
The questions in this assignment come from this lesson. Read it in the MTH621 handout before you open the assignment file, then practise it with the MCQs and past papers.
Solution
The solution has not been added yet. Request it from the download box and it will be added to this page, usually within a day.
Before you submit on VULMS
- 1 Start on the questions in the assignment file now. The solution will be added to this page once it is written.
- 2 Write the final answer in your own words. VU checks assignments for copying, and copied work gets zero marks.
- 3 Save your answer in the file type the assignment file asks for, and name it with your student ID, for example BC260012345.
- 4 Open the file once more to check it is not empty or corrupted, then upload it on VULMS before 11:59 pm on Fri 13 Nov.
Questions about this assignment
When is MTH621 Assignment 1 due?
Friday 13 November 2026 at 11:59 pm. VULMS does not accept files after the deadline.
When will the solution be added?
Most solutions are up within a day of a request. Requests tell us which ones to write first, and 1 student has asked for this one so far.
Can I submit the solution as it is?
No. VU checks assignments for copying, and copied work gets zero marks. Use the solution to check your method, then write your own answer.
What file do I submit?
The assignment file says which file type to upload and lists any extra instructions from your instructor. Name the file with your student ID before you upload it on VULMS.