Science:Math Exam Resources/Courses/MATH103/April 2011/Question 01 (a)
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Question 01 (a) 

For each of the following series, indicate whether or not they converge: 
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 

and are both standard. A constant factor () does not change the convergence behavior. Also recall the geometric series , and that the convergence here depends on the value of . For the last example, compare it to a classical series above. 
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Solution 

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valid since for all and thus (then rearrange this last inequality to get the above displayed equation). Therefore, the series
converges. Then, we know that is absolutely convergent and hence convergent. 