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Unformatted text preview: olute value of the terms and see if that series converges by other tests we have seen (note that this prohibits the use of alternating series test, so we must use one of the other tests we have seen). If it converges, we are done and the series is absolutely convergent.
Step 2: If the series is not absolutely convergent, then try to prove that the series is convergent on its own (most notably, we will most likely be able to use the alternating series test here). If the series converges without using the absolute values, then the series is conditionally convergent.
Step 3: If it fails both steps above, then we simply say the series is divergent. Example 1
Determine if the following series converges absolutely, conditionally, or diverges:
n 3 2n 1 (1) n5 3n 2 2
n2 n First we check for absolute convergence, we get: n 3 2n 1
n 3 2n 1 | (1) n5 3n 2 2 | n5 3n 2 2
n2 n n3
Here we see that this will be a comparison test where we compare to: 5 2
n2 n We perform the limit comparison...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.
- Summer '00
- Calculus, SmartPen Lectures, Lecture Notes, MATH1004, Kyle Harvey