# Alternating Series Test Fails

1. Apr 4, 2013

### whatlifeforme

1. The problem statement, all variables and given/known data
determine either absolute convergence, conditional convergence, or divergence for the series.

2. Relevant equations
$\displaystyle \sum^{∞}_{n=1} (-1)^n \frac{6n^8 + 3}{3n^5 + 3}$

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?

2. Apr 4, 2013

### Staff: Mentor

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.

3. Apr 4, 2013

### whatlifeforme

can i use the divergence test?

4. Apr 4, 2013

### Infrared

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

5. Apr 4, 2013

thanks.