Science:Math Exam Resources/Courses/MATH220/April 2005/Question 07
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Question 07 

Determine whether the series converges or diverges; prove your answer. 
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 

What convergence tests do you know of? Which one might apply well in this case? 
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. Using the ratio test seems appropriate here. If we denote the general term of the series by Then the ratio test asks us to look at (Note: we removed the absolute value since the terms are clearly all positive). And so Since this is a number less than one, the ratio test guarantees that the series converges absolutely. 