given that {a_n} is a sequence of numbers that are greater than 0 and that sum a_n diverges. show that sum a_n / (1+ a_n) diverges. how do i show that? i know that a_n / (1+ a_n) = 1- 1/ (1+ a_n) but what else?
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We can break the problem into two cases. Case 1: Suppose that . Then, But then the terms of the sum on the right do not approach zero either, so the sum is divergent. Case 2: Suppose that . Try using the limit comparison test.
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