Given an infinite series, I can check the conditions required for application of the Comparison Tests. I can find a related series to which applying the Direct Comparison Test or the Limit Comparison Test determines the convergence or divergence of the original series. Determine if the following series converge or diverge. The question will indicated which test to use. If not test is indicated, you may use your choice of the limit comparison test (LCT) or the direct comparison test (DCT). In your writing, you may refer to the tests using the abbreviations. 1 3/2 - 1 5k +3 , using DCT. k=1 2. (3k2 + k + 1) -1/2 , using LCT. k=1