Consider the following infinite series, where the constant A0 6 R'\": i: a :\" A\") k _ (k + 1) 536+2 (a) What is (\"k\") equals to? Simply your answer as much as possible. Show all your steps. [3 marks] at k+1 at (b) What is equals to? Simply your answer as much as possible. Show all your steps. [2 marks] k+1 \"k (c) What is L = lim k-+m equals to? Justify your answer. Show all your steps. [2 marks] (d) Using the ratio test. what is the range for A0 such that the innite series converge? Justify your answer. Show all your steps. [1 mark] (e) Using the ratio test. what is the range for A0 such that the innite series guerge? Justify your answer. Show all your steps. [1 mark] (f) What is the range for A; such that the innite series' convergence or divergence is inconclusive by the ratio test? Justify your answer. Show all your steps. [1 mark]