Answer Happy

3 (8 pts) This problem consists of two multiple choice questions. On your paper, just write the question number, and give your answer. (a) For which one of the following series is the ratio test inconclusive? (i) n=1∑∞​5nn​ (ii) n=1∑∞​n​(−3)n+1​ (iii) n=1∑∞​1+n2n​ (iv) n=1∑∞​n​n!​ (b) Does the sequence whose nth term is an​=arctannln(e+n1​)​ converge and if so to what value? (i) No it diverges. (iii) Yes, it converges to 0 . (ii) Yes, it converges to π. (iv) Yes, it converges to π2​.