Science:Math Exam Resources/Courses/MATH103/April 2015/Question 01 (a) (ii)
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Question 01 (a) (ii) 

Given the following general terms determine whether the corresponding sequences are converging, diverging, and/or bounded. (do not calculate the limit of converging sequences.)
(ii) 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

What is ? How does change the limit? 
Hint 2 

Can you find a bound for ? 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We have , since for all n, thus by dividing both sides by we have , so , which mean that the sequence is bounded.
It is obvious that , however is either 1 or 1 for even and odd values of n, this causes the limit value to be , so there is no unique limit which implies that the sequence diverges. 