Problem 3. (18 points) Determine whether each of the following series converges or diverges. Provide a careful proof; in particular: ido 1. Clearly state which test you are using and check whether the hypotheses are satisfied. Justify why each of the hypotheses are satisfied (for example, justify why a function is decreasing). 2. Depending on the test used, compute limits or improper integrals using correct notation and/or provide a careful argument about the convergence or divergence of the "new" series. 3. Provide clear conclusions, including the test(s) used, and make sure that it is clear which series you are saying converges or diverges and for which reason. Use complete sentences. OO 2k a. VK6 + k+1e 5n b. (3n)! n=1-1) n C. M n=2 (1 + Inn 2