009C Sample Midterm 3, Problem 1 Detailed Solution

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Test if the following sequence converges or diverges.

If it converges, also find the limit of the sequence.

Background Information:  
L'Hôpital's Rule, Part 2

        Let    and    be differentiable functions on the open interval    for some value   

        where    on    and    returns either    or   


Step 1:  
First, let  
Step 2:  
Therefore, the sequence converges.
Additionally, the limit of the sequence is

Final Answer:  
        The sequence converges. The limit of the sequence is  

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