Science:Math Exam Resources/Courses/MATH101/April 2013/Question 09 (a)
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Question 09 (a) 

FullSolution Problems. In questions 4–12, justify your answers and show all your work. If a box is provided, write your final answer there. Unless otherwise indicated, simplification of numerical answers is required in these questions. 'Determine, with explanation, whether the following 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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

First, write the series in terms of summation notation. 
Hint 2 

Try the pseries test with the comparison test. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. This is the series Notice for all , and diverges by pseries (it's just a multiple of the harmonic series). Then by the comparison test, the series diverges. 