Science:Math Exam Resources/Courses/MATH220/December 2009/Question 08 (a)
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Question 08 (a) 

Suppose that . Prove that if is a bounded sequence then 
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 

A real sequence is bounded if there exist real numbers and such that

Hint 2 

The first hint suggests using the Squeeze Theorem. 
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. Using the hint, we see that there exist real numbers and such that Notice that Thus by the Squeeze Theorem, we see that as required. 