The discussion revolves around determining the convergence or divergence of the series \(\sum^{∞}_{n=1} (-1)^n \frac{6n^8 + 3}{3n^5 + 3}\). Participants are exploring concepts related to series convergence, particularly focusing on absolute and conditional convergence.
The discussion includes various interpretations of the series behavior, with some participants suggesting that the terms do not approach zero, which may indicate divergence. However, there is no explicit consensus on the final conclusion regarding convergence or divergence.
Participants mention constraints related to the alternating series test and the behavior of the sequence involved, indicating a focus on the properties of the series terms.
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
\displaystyle \sum^{∞}_{n=1} (-1)^n \frac{6n^8 + 3}{3n^5 + 3}
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.