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Test the series for convergence or divergence.

$ -\frac {2}{5} + \frac {4}{6} - \frac {6}{7} + \frac {8}{8} - \frac {10}{9} + \cdot \cdot \cdot $

divergent

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Let's see whether the Siri's converges are emerges. Now we see that it's alternating. However we see that the numerator increases no sloppy there, let me backtrack. Increases by two, whereas the denominator increases on ly by one so we can actually rewrite this Erie's Yeah, let's say up top. First of all, we should have this negative one to the end power and then up top. We should have two in and then in the denominator, we're adding one each time. But we're starting with an equals one. So four plus end. So here, let's just look at this term here are in. And then let's just go find B End to just be to win over four percent. Now I know that the limit of the end is just equal to two, which is non zero. So this implies that the limit of A M is undefined sense. As n gets really, really large way want will keep all supplying by negative one. But this fraction over here is getting closer to to sew in the limit. A N is getting very close to negative two two negative to two and so on. It's all the limit just will not exist. Therefore, our Siri's we're given above diverges bye, the diversions test, and that's our final answer