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Test the series for convergence or divergence.

$ \displaystyle \sum_{n = 1}^{\infty} (-1)^n \frac {3n - 1}{2n + 1} $

diverges

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Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

Boston College

Let's test the Siri's for convergence or diversions. Now, if we just look at this term over here in this fraction, the women is and goes to infinity ofthree and minus one, two, one plus one. You can use lope. It's hell here to get three halfs and the limit, which is not equal to zero. Therefore, if we continue to multiply this by negative one to the end, that just tells us that for a large and and values negative one to the end. Three and minus one sue one plus one Ossa lates between three halfs and negative three house or US oscillator around east, two numbers. So this just means that the limit of our a end, which is the entire term here limit of an which is the limit as N goes to infinity of negative one to the end three and minus one to one plus one. It does not exist in particular. It's not equal to zero. So the Siri's diverges bye with the author calls the diversions test, and that's the final answer