What does this series do: ∞∑ 8/ (3n2+ 2n+1)=1?

Converge

Correct Answer: Converge. 1. Since the nth term divergence test does not work, the easiest way to do this is by the Direct Comparison Test: 8/(n^2)> 8/(3n^2+2n+1) 2. P-Series: 8/n^2 and 2>1 so 8/n^2 converges 3. Since 8/n^2 converges so does the given series since it is smaller Wrong Answers: Diverge. There are not too many ways to come up with this conclusion. However a common mistake is that when you use any type of comparison test, you must make sure you are comparing a series to the same degree. For example in this problem if you compared the series to 8/n rather than 8/(n^2) you would have come that 8/n diverges. And even though that is true you may also make the mistake of saying the the given series also diverges, although you cannot compare those two series because the greater diverges, so the smaller could converge or diverge. However both of those mistake are fairly common. Cannot Be Determined. You may conclude that it cannot be determine because there are restrictions on the direct comparison test (as I just described above). For example, if some series a diverges, and a>b then you could not conclude that series b also diverges. However, that rule does not apply for converging series, but the rule is in fact the opposite. It is a common mistake to mix up those rules for comparing converging and diverging series.