If someone could help me out with this problem and include s

If someone could help me out with this problem, and include some explanations that would be great.

The series is absolutely convergent. The series converges, but not absolutely. The series diverges. The alternating series test shows the series converges. The series is a \\(p\\)-series. The series is a geometric series. We can decide whether this series converges by comparison with a \\(p\\) series. We can decide whether this series converges by comparison with a geometric series. Partial sums of the series telescope. The terms of the series do not have limit zero. None of the above reasons applies to the convergence or divergence of the series.

Solution

1) the series diverges

2)the series converges but not absolutely

3)the series diverges

4)the series diverges

5)the series diverges

6)the series absolutely convergent