Consider the following infinite series: (13 + 1) gk = k=2 k=2 In (1:5 - V5) (a) Is the sequence rule gk > 0 ? Justify your answer. Show all your steps. [1 mark] (b) Find a simpler sequence hx related to gx. Show all your steps. [2 marks] (c) Is hk > 0 ? Justify your answer. Show all your steps. [1 mark] (d) Is gx 2 hk Or hx 2 9k ? Justify your answer. Show all your steps. [2 marks] (e) Does the series related to hx converge or diverge? Justify your answer. Show all your steps. [2 marks] (f) Using the direct comparison test, what can you say about the convergence or divergence of the series with gx ? Justify your answer. Show all your steps. [2 marks]