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
+
+ ··· .
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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
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.
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.
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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?
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(c) What happens in the long run? That is, how much of the drug remains in the body
as n → ∞?
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