Precalculus Enhanced with Graphing Utilities, Books a la Carte Edition Plus NEW MyLab Math -- Access Card Package (7th Edition)
7th Edition
ISBN: 9780134268231
Author: Michael Sullivan, Michael Sullivan III
Publisher: PEARSON
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Textbook Question
Chapter B, Problem 20SB
In Problems 5-28, determine whether each sequence converges or diverges. If it converges, find its limit.
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Book Problem 15
Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the
quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as
"DIV".
an=
b₁ =
(-1)"n³
2n5+8n² + 2
(-1)"n7
2n7+8n²+2
1. Write the first four terms of the sequence given by
(−1)” (2n +1)² [°
22n-1 + (−1)n+¹ n=1
If it converges, find the value of its limit.
(a) Show that if n € N, then <¹dx.
(b) Conclude that the sequence (an) is a decreasing sequence, where
an = 1+ +
n+
1
n
In n.
Chapter B Solutions
Precalculus Enhanced with Graphing Utilities, Books a la Carte Edition Plus NEW MyLab Math -- Access Card Package (7th Edition)
Ch. B - If a sequence { S n } converges to L , we call L...Ch. B - If a 1 , a 2 ,..., a n ,... is some collection of...Ch. B - Prob. 3CVCh. B - Prob. 4CVCh. B - Prob. 5SBCh. B - Prob. 6SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 10SB
Ch. B - Prob. 11SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 15SBCh. B - Prob. 16SBCh. B - Prob. 17SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 19SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - Prob. 21SBCh. B - Prob. 22SBCh. B - Prob. 23SBCh. B - Prob. 24SBCh. B - Prob. 25SBCh. B - Prob. 26SBCh. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 5-28, determine whether each sequence...Ch. B - In Problems 29-32, find the first five terms in...Ch. B - In Problems 29-32, find the first five terms in...Ch. B - Prob. 31SBCh. B - In Problems 29-32, find the first five terms in...
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- Find the first 4 terms of the sequence defined byf (n) = 1/2n+ n.arrow_forwardProblem 2. Let {a, }, be a sequence of real numbers defined by 2n+1 a1 = 1, an an-1, n= 2,3,4, 3n Show that the sequence {a, }n converges and find its limit.arrow_forwardThe first term of a sequence is x1 = 1. Each succeeding term is the sum of all those that come before it: xn+1 = x1 + x2 + g + xn. Write out enough early terms of the sequence to deduce a general formula for xn that holds for n ≥ 2.arrow_forward
- Answer the following problems directly. 1-Let F(n) be the nth term of the Fibonacci sequence, With F(1) = 1, F(2) = 1, F(3) = 2, and so on. %3D %3D 1. Find F (8) 2. Find F(19) 3. IfF (22) = 17,711 and F(24) = 46,368, %3D what is F(23)?arrow_forward2. Find and prove a closed formula for the recursive sequence a, = 3, a, =ai-2arrow_forwardProblem 58. Consider the sequence given by the piecewise defined function when k is even Pk: when k is odd k+1 Prove that {pk}1 converges to 0.arrow_forward
- Problem 3. Define the integer sequence Lo, L1, L2, , recursively by Lo = 2, L1 = 1, and %3D •... Ln+2 = Ln+1 + Ln , for n > 0. Prove that L + L + …+ L = L„Ln+1– 2, for n > 1. ...arrow_forward2. Consider the sequence {10, -2,0.4, -0.08, ...} (a) Find a formula for the general term an of the sequence, assuming that the pattern of the given terms continue. (b)Determine whether or not the sequence converges or diverges. If it converges, find its limit.arrow_forward7. Find a formula for a, of the sequence { 3, 6, 9, 12, ..}, assuming that the pattern of the first few terms continues. Determine whether the sequence converges or diverges. Why? If it converges, find the limit.arrow_forward
- 5. Give a summation-free formula for the ordinary and exponential generating functions for each sequence. (a) an = (-1)". (This sequence alternates 1, −1, 1, −1, … …..) (b) bn = n. (This sequence begins 0, 1, 2, 3,... and continues on forever. For both functions, you may want to factor an x out of the infinite sum.)arrow_forwardSOLVE STEP BY STEP IN DIGITAL FORMATarrow_forwardMany people take a certain pain medication as a preventative measure for heart disease. Suppose a person takes 70 mg of the medication every 24 hr. Assume also that the medication has a half-life of 24 hr; that is, every 24 hr half of the drug in the blood is eliminated. Complete parts a. and b. below. a. Find recurrence relation for the sequence {d} that gives the amount of drug in the blood after the nth dose, where d₁ = 70. O A. dn+1=dn +70 O B. dn+1=2dn - 70 1 OC. dn+1=dn-140 O D. dn+1=2dn + 140 b. Using a calculator, determine the limit of the sequence. In the long run, how much drug is in the person's blood? Confirm the result by finding the limit of the sequence directly. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The limit of the sequence is mg. O B. The limit does not exist.arrow_forward
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