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Math 1320: Lab 4 Name/Unid: 1. Determine whether the sequence is convergent or divergent. (a) {an } = e1/n . (b) {an } = (−1)n−1 n . n2 +1 2. Determine whether the series is convergent or divergent. If it converges, find the sum. P∞ √1 (a) n=0 ( 3)n . (b) The geometric series given by: 4+3+ 9 27 + + ··· . 4 16 3. Find the values of α for which the series converges. Then, find the sum of the series for those values of α. ∞ X (α + 1)n n=1 4n Page 2 . P P∞ P∞ 4. Suppose ∞ n=1 an diverges and n=1 bn diverges. Does n=1 (an + bn ) necessarily diverge? If so, prove it. If not, provide a counterexample and explain. Page 3 5. A patient is prescribed a drug and is told to take one 50-mg pill every six hours. After six hours, about 7% of the drug remains in the body. (a) What quantity of the drug remains in the body after the patient takes four pills? (b) What quantity remains after n pills are taken? Page 4 (c) What happens in the long run? That is, how much of the drug remains in the body as n → ∞? Page 5