Science:Math Exam Resources/Courses/MATH103/April 2014/Question 04 (b)
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Question 04 (b) 

Let be a sequence, where . Find the limit of the sequence if it converges, or show that it diverges, otherwise. Work must be shown for full marks. Simplify fully. 
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 

Expand the factorial and cancel a common term in the numerator and denominator. 
Hint 2 

Keep in mind is equivalent to 
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
Cancelling the common factor in the numerator and denominator, we get
As , the numerator () of the last expression is constant, while the denominator () tends to . Thus,
We conclude that . 