Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (c) (i)
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Question 02 (c) (i) 

For each of the following series, choose the appropriate statement. (Write N, O, P, S, or T in each box; each answer will be used at most once, and each series matches a single answer only.) N: The series converges by the Ratio Test. O: The series converges absolutely by the Comparison Test with a pseries. P: The series converges by the Alternating Series Test. S: The series diverges. T: The series converges by the Integral Test. (i) 
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Hint 

Look for a nice substitution. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since the function is positive and decreasing on , we can consider the integral test, According to the test, the series converges if To evaluate this integral, substitute , . This simplifies to This is indeed convergent, hence the answer is .
