A doctor prescribes a 400 mg antibiotic tablet to be taken every eight hours. It is known that the body eliminates 80% of the drug in eight hours. (a) How much of the drug is in the body just after the second tablet is taken? After the third tablet? second tablet 480 third tablet 496 mg mg (b) If Q, is the quantity of the antibiotic in the body just after the nth tablet is taken, find an equation that expresses Qn + 1 in terms of Qn- Qn+ 1 = (0.2+400) X (c) What quantity of the antibiotic remains in the body in the long run? 500 mg Σοπ Suppose Σan Σb, and Σ b, are series with positive terms and Σb, is known to be convergent. n (a) If an > bn for all n, what can you say about Σ an? Why? Σa, diverges by the Comparison Test. OΣan converges if and only if an ≤ 2bn ΟΣ ח ○ We cannot say anything about Σ an OΣa, converges if and only if an ≤ 4bn. n OΣa, converges by the Comparison Test. ΟΣΟΝ X Σan? (b) If aɲ < b for all n, what can you say about Σ an? Why? n OΣan converges by the Comparison Test. ΟΣΟΝ OΣa, converges if and only if ΟΣΟΝ bn sansb 2 OΣa, diverges by the Comparison Test. ΟΣΟΝ Σαπ ● We cannot say anything about Σ an ΟΣ an converges if and only if bn 4 S X
A doctor prescribes a 400 mg antibiotic tablet to be taken every eight hours. It is known that the body eliminates 80% of the drug in eight hours. (a) How much of the drug is in the body just after the second tablet is taken? After the third tablet? second tablet 480 third tablet 496 mg mg (b) If Q, is the quantity of the antibiotic in the body just after the nth tablet is taken, find an equation that expresses Qn + 1 in terms of Qn- Qn+ 1 = (0.2+400) X (c) What quantity of the antibiotic remains in the body in the long run? 500 mg Σοπ Suppose Σan Σb, and Σ b, are series with positive terms and Σb, is known to be convergent. n (a) If an > bn for all n, what can you say about Σ an? Why? Σa, diverges by the Comparison Test. OΣan converges if and only if an ≤ 2bn ΟΣ ח ○ We cannot say anything about Σ an OΣa, converges if and only if an ≤ 4bn. n OΣa, converges by the Comparison Test. ΟΣΟΝ X Σan? (b) If aɲ < b for all n, what can you say about Σ an? Why? n OΣan converges by the Comparison Test. ΟΣΟΝ OΣa, converges if and only if ΟΣΟΝ bn sansb 2 OΣa, diverges by the Comparison Test. ΟΣΟΝ Σαπ ● We cannot say anything about Σ an ΟΣ an converges if and only if bn 4 S X
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.57TI: What is the total effect on the economy of a government tax rebate of $1,000 to each household in...
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Transcribed Image Text:A doctor prescribes a 400 mg antibiotic tablet to be taken every eight hours. It is known that the body eliminates 80% of the drug in eight hours.
(a) How much of the drug is in the body just after the second tablet is taken? After the third tablet?
second tablet
480
third tablet
496
mg
mg
(b) If Q, is the quantity of the antibiotic in the body just after the nth tablet is taken, find an equation that expresses Qn + 1 in terms of Qn-
Qn+ 1 = (0.2+400)
X
(c) What quantity of the antibiotic remains in the body in the long run?
500
mg
Transcribed Image Text:Σοπ
Suppose Σan Σb,
and Σ b, are series with positive terms and Σb, is known to be convergent.
n
(a) If an > bn for all n, what can you say about Σ an? Why?
Σa, diverges by the Comparison Test.
OΣan converges if and only if an ≤ 2bn
ΟΣ
ח
○ We cannot say anything about Σ an
OΣa, converges if and only if an ≤ 4bn.
n
OΣa, converges by the Comparison Test.
ΟΣΟΝ
X
Σan?
(b) If aɲ < b for all n, what can you say about Σ an? Why?
n
OΣan converges by the Comparison Test.
ΟΣΟΝ
OΣa, converges if and only if
ΟΣΟΝ
bn
sansb
2
OΣa, diverges by the Comparison Test.
ΟΣΟΝ
Σαπ
● We cannot say anything about Σ an
ΟΣ an converges if and only if
bn
4
S
X
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