The first sum seems to be (I assume here that you meant the index to be k and not n...), and if this is so the sum can't converge since

the limit of its general term is not zero: , and with the alternating sign the general term doesn't even diverge to infinity.

About the second one: it converges conditionally since it is a Leibnitz series, but taking its general term's absolute value we get:

, and by the comparison test with the harmonic series it diverges.

Tonio