This is a similar question that I have to the other one that I posted. Determine if the following series converges or diverges. sum[k=1,inf] 3/(k(k+3)) I applied the limit comparison test with 1/k^2 also k(k+3))=k^2+3k lim k->inf [ 3/(k^2+3k) ]/[ 1/k^2 ] = lim k->inf (3k^2/(k^2+3k) =H 3 because sum[k=1,inf] 1/k^2 is a convergent p-series than sum[k=1,inf] 3/(k(k+3)) must also converge by the limit comparison test. I plugged this into wolfram alpha sum[n=1,inf] of 3/(k(k+3)) and it said that the sum does not converge by the limit comparison test. Am I doing something wrong? Thanks for any help.