Science:Math Exam Resources/Courses/MATH105/April 2017/Question 05 (c)
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Question 05 (c) 

Determine whether the series converges or diverges. 
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 

When you are trying to determine whether a series with exponential functions and factorials converges, you should consider using the ratio test. 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. In order to show that the series converges, we use the ratio test: 