Science:Math Exam Resources/Courses/MATH105/April 2016/Question 05 (c)
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Question 05 (c) 

Determine whether the following series converge or diverge. (c) . 
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? 
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Hint 

Can we apply the integral test? 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Before we apply the integral test, let's check whether satisfies the assumptions of the test. First, the function is continuous and nonnegative for . (In fact, this is even true for since for .) Also, since for , the function is in particular decreasing for . Therefore, the integral test is applicable to . Using the substitution , we have The integral test then implies that the series diverges. 