1. LIMIT COMPARISON TEST The Limit Comparison Test is most often used when the limit L = lim ak lies in the interval (0, co). In the case where L is k-+00 bk zero or infinity, we can still compare _ ax, and _ be, but only with additional assumptions. Theorem. [Limit Comparison Test: 0-co cases) Suppose that ax > 0 and be > 0 for all k 2 N, where N is a positive integer. . [0 CASE] IF lim " = 0 AND ~ be converges THEN Eax converges. k-+0o bk . [.-CASE] IF lim ak = 0 AND _ bx diverges THEN Cax diverges. k-+00 0k In preparation for using this theorem in the Lab, evalute the following limits. (1) Compute In k lim *-+00