MATH101 April 2012
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Question 04 (c)
Determine, with explanation, whether the series
converges absolutely, converges conditionally, 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?
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Can you integrate ?
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We will use the integral test. Note that
We can calculate by substitution with (then du=(1/x)dx) to get
This implies that the series converges absolutely by the integral test.
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