Having trouble with this Calculus Problem Below... Can anyone solve and please show work?

Question

Choose the infinite series which diverges from the four infinite series listed below. (The answer slot is above the series.) If you think that they all converge, choose the answer: "The above series all converge." If you think that at least two of the series diverge, choose the answer: "At least two of the above series diverge."

possible solutions from the back of the book...

oo
∑ (-1)^n (n^-3)
n=1

oo
∑ (n^-3)
n=1

oo
∑ (-1)^n / (ln n)
n=2

oo
∑(-1)^n / (n ln n)
n=2

or the above series all converge.

or could it be at least two of the above series diverge.

Answer 1

Actually, all of the above series converge. The first two converge absolutely by the p-series test. The second two converge conditionally by the alternating series test.

Answer 2

at least two of the above series diverge.