Science:Math Exam Resources/Courses/MATH103/April 2017/Question 01 (a)
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) (i) • Q1 (e) (ii) • Q1 (e) (iii) • Q1 (f) • Q2 (a) • Q2 (b) (i) • Q2 (b) (ii) • Q2 (c) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q4 • Q5 • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q8 (c) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • Q9 (e) •
Question 01 (a)  

Given the following general terms , determine whether the corresponding sequences are converging, diverging, monotone (increasing or decreasing) and/or bounded. Check all boxes that apply.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

If a sequence has a limit, we say the sequence is convergent, and that the sequence converges to the limit. Otherwise, the sequence is divergent. A monotone sequence: such that either (1) for every , or (2) for every . A bounded sequence: A sequence is said to be bounded if such that for all positive integers 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution  

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. (i): when , sequence gets smaller, and goes to to 0. Thus monotone and convergent. , the largest one is , bounded. (ii) , so sequence will never converge to a limit (it will change switch between "2" and "0" ). But it do have a upper bound which is 2. (iii) . 1 is a constant, just leave it there. gets smaller with n increase, until converge to a limit 0. the range for is (0,0.5]. (iv) The graph of is monotone increasing. Thus it is not convergent and do not have a bound.
