The alternating series test for convergence lets us say whether an alternating series is converging or diverging. When we use the alternating series test, we need to make sure that we separate the series a_n from the (-1)^n part that makes it alternating.
Read MoreIf we say that a sequence converges, it means that the limit of the sequence exists as n tends toward infinity. If the limit of the sequence as doesn’t exist, we say that the sequence diverges.
A sequence always either converges or diverges, there is no other option. This doesn’t mean we’ll always be able to tell whether the sequence converges or diverges, sometimes it can be very difficult for us to determine convergence or divergence.
Read MoreThe comparison test for convergence lets us determine the convergence or divergence of the given series by comparing it to a similar, but simpler comparison series. We’re usually trying to find a comparison series that’s a geometric or p-series, since it’s very easy to determine the convergence of a geometric or p-series.
Read MoreBefore we can learn how to determine the convergence or divergence of a geometric series, we have to define a geometric series. Once you determine that you’re working with a geometric series, you can use the geometric series test to determine the convergence or divergence of the series.
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