someone help me please! thank you so much!

1. Does the series > In (n) ") converge or diverge? In order to receive any credit for this question you MUST provide a rigorous mathematical proof that fully justifies your answer. 2. Consider the following sequence given recursively as: do = 1 and a,,. = In (e"" -a,, ) when n 2 0. Suppose N is a positive integer. (a) Prove that if ay > 0, then aN+1 > 0. N (b) Prove that Car =e-e"N. . k=0