Since the sequence (apart from the (-1)n factor) is increasing, doesn't that give you a hint as to what the series is doing? It might help to write a few terms in the series.whatlifeforme said:Homework Statement
determine either absolute convergence, conditional convergence, or divergence for the series.
Homework Equations
[itex]\displaystyle \sum^{∞}_{n=1} (-1)^n \frac{6n^8 + 3}{3n^5 + 3} [/itex]
The Attempt at a Solution
I cannot use the alternating series test since the function is increasing not decreasing.What should i do next?
HS-Scientist said:Yep, it diverges since its terms do not approach zero.
The Alternating Series Test is a mathematical test used to determine the convergence or divergence of an infinite series. It specifically applies to alternating series, where the signs of the terms alternate between positive and negative.
The Alternating Series Test states that if a series alternates in sign and each term is smaller than the previous term, then the series will converge. This means that the terms must eventually approach zero as the series continues.
The Alternating Series Test may fail in two cases: when the series does not alternate in sign, or when the terms do not decrease in magnitude. In these cases, the test cannot be used to determine the convergence or divergence of the series.
Yes, there are a few exceptions to the Alternating Series Test. For example, if the series is a geometric series or a telescoping series, the test may not be applicable. In these cases, other tests must be used to determine convergence or divergence.
The Alternating Series Test is important because it provides a simple and efficient way to determine the convergence or divergence of an infinite series. It is also a useful tool in many other mathematical and scientific applications, such as in the analysis of alternating currents in electrical engineering.