What is the next step for determining convergence or divergence of this series?

[whatlifeforme]

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?

 

[Mark44]

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?

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]

can i use the divergence test?

 

[Infrared]

Yep, it diverges since its terms do not approach zero.

 

[whatlifeforme]

Yep, it diverges since its terms do not approach zero.

thanks.