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## Main Question or Discussion Point

I need help identifying if it converges or diverges or conditionally converges.

[tex]\Sigma[/tex][tex](-1)^{k}[/tex][tex]\frac{(k+4)}{(k^{2}+k)}[/tex]

First I want to test for absolute convergence, and comparing this limit to 1/k I get that it diverges. Since it diverges, I need to test it now using the Alternating Series test, in which the limit is 0 and it converges. So my question is, does it conditionally converge?

[tex]\Sigma[/tex][tex](-1)^{k}[/tex][tex]\frac{(k+4)}{(k^{2}+k)}[/tex]

First I want to test for absolute convergence, and comparing this limit to 1/k I get that it diverges. Since it diverges, I need to test it now using the Alternating Series test, in which the limit is 0 and it converges. So my question is, does it conditionally converge?