2. In each of the following, if the given statement is true in general, then mark...

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2. In each of the following, if the given statement is true in general, then mark the O to the left of TRUE with a vand fill in the blank with the name of a test; otherwise, mark the to the left of FALSE with a v and give a counterexample. (a) If ) an converges, then Jan converges. n=1 n=1 O TRUE, as can be shown using O FALSE, because because it does not hold for an = for n >1 (Ь) If an converges, then Janl diverges. n=1 n=1 O TRUE, as can be shown using O FALSE, because because it does not hold for an = for n >1 (c) If ) an (r – 4)" converges at r = 8, then it converges at r = 0. n=0 O TRUE, as can be shown using O FALSE, because it does not hold for an = for n > 1. 2. In each of the following, if the given statement is true in general, then mark the O to the left of TRUE with a vand fill in the blank with the name of a test; otherwise, mark the to the left of FALSE with a v and give a counterexample. (a) If ) an converges, then Jan converges. n=1 n=1 O TRUE, as can be shown using O FALSE, because because it does not hold for an = for n >1 (Ь) If an converges, then Janl diverges. n=1 n=1 O TRUE, as can be shown using O FALSE, because because it does not hold for an = for n >1 (c) If ) an (r – 4)" converges at r = 8, then it converges at r = 0. n=0 O TRUE, as can be shown using O FALSE, because it does not hold for an = for n > 1.