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Math
Advanced Math
4(1). Find the Laurent series expansion for (22-1)(+2) in the annulus {1 < [z] <2}.
4(1). Find the Laurent series expansion for (22-1)(+2) in the annulus {1 < [z] <2}.
BUY
College Algebra
1st Edition
ISBN:
9781938168383
Author: Jay Abramson
Publisher:
OpenStax
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1 Prerequisites
2 Equations And Inequalities
3 Functions
4 Linear Functions
5 Polynomial And Rational Functions
6 Exponential And Logarithmic Functions
7 Systems Of Equations And Inequalities
8 Analytic Geometry
9 Sequences, Probability And Counting Theory
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9.1 Sequences And Their Notations
9.2 Arithmetic Sequences
9.3 Geometric Sequences
9.4 Series And Their Notations
9.5 Counting Principles
9.6 Binomial Theorem
9.7 Probability
Chapter Questions
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Problem 1RE: Write the first four terms of the sequence defined by the recursive formula a1=2,an=an1+n.
Problem 2RE: Evaluate 6!(53)!3!
Problem 3RE: Write the first four terms of the sequence defined by the explicit formula a an=10n+3 .
Problem 4RE: Write the first four terms of the sequence defined by the explicit formula an=n!n(n+1).
Problem 5RE: Is the sequence 47,4721,8221,397,... arithmetic? If so, find the common difference.
Problem 6RE: Is the sequence 2,4,8,16,... arithmetic? If so, find the common difference.
Problem 7RE: An arithmetic sequence has the first term a1=18 and common difference d=8 . What are the first five...
Problem 8RE: An arithmetic sequence has terms a3=11.7 and a8=14.6 . What is the first term?
Problem 9RE: Write a recursive formula for the arithmetic sequence 20,10,0,10,...
Problem 10RE: Write a recursive formula for the arithmetic sequence 0,12,1,32,... , and then find the 31stterm.
Problem 11RE: Write an explicit formula for the arithmetic sequence 78,2924,3724,158,...
Problem 12RE: How many terms are in the finite arithmetic sequence 12,20,28,...,172 ?
Problem 13RE: Find the common ratio for the geometric sequence 2.5,5,10,20,...
Problem 14RE: Is the sequence 4,16,28,40,... geometric? If so find the common ratio. If not, explain why.
Problem 15RE: A geometric sequence has terms a7=16,384 and a9=262,144 . What are the first five terms?
Problem 16RE: A geometric sequence has the first term a1=3 and common ratio r=12 What is the 8thterm?
Problem 17RE: What are the first five terms of the geometric sequence a1=3,an=4an1
Problem 18RE: Write a recursive formula for the geometric sequence 1,13,19,127,...
Problem 19RE: Write an explicit formula for the geometric sequence 15,115,145,1135,...
Problem 20RE: How many terms are in the finite geometric sequence 5,53,59,...,559,049
Problem 21RE: Use summation notation to write the sum of terms 12m+5 from m=0 to m=5 .
Problem 22RE: Use summation notation to write the sum that results from adding the number 13 twenty times.
Problem 23RE: Use the formula for the sum of the first ii terms of an arithmetic series to find the sum of the...
Problem 24RE: A ladder has 15 tapered rungs, the lengths of which increase by a common difference. The first rung...
Problem 25RE: Use the formula for the sum of the first nterms of a geometric series to find S9 , for the series...
Problem 26RE: The fees for the first three years of a hunting club membership are given in Table 1. If fees...
Problem 27RE: Find the sum of the infinite geometric series k145(13)k=1.
Problem 28RE: A ball has a bounce-back ratio 35 . of the height of the previous bounce. Write a series...
Problem 29RE: Alejandro deposits $80 of his monthly earnings into an annuity that earns 6.25% annual interest,...
Problem 30RE: The twins Sarah and Scott both opened retirement accounts on their 2lst birthday. Sarah deposits...
Problem 31RE: How many ways are there to choose a number from the set 10,6,4,10,12,18,24,32 that is divisible by...
Problem 32RE: In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How...
Problem 33RE: How many ways are there to construct a 4-digit code if numbers can be repeated?
Problem 34RE: A palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades...
Problem 35RE: Calculate P(18,4) .
Problem 36RE: In a group of 5 freshman, 10 sophomores, 3 juniors, and 2 seniors, how many ways can a president,...
Problem 37RE: Calculate C(15,6)
Problem 38RE: A coffee shop has 7 Guatemalan roasts, 4 Cuban roasts, and 10 Costa Rican roasts. How many ways can...
Problem 39RE: How many subsets does the set 1,3,5,...,99 have?
Problem 40RE: A day spa charges a basic day rate that includes use of a sauna, pool, and showers. For an extra...
Problem 41RE: How many distinct ways can the word DEADWOOD be arranged?
Problem 42RE: How many distinct rearrangements of the letters of the word DEADWOOD are there if the arrangement...
Problem 43RE: Evaluate the binomial coefficient (823) .
Problem 44RE: Use the Binomial Theorem to expand (3x+12y)6
Problem 45RE: Use the Binomial Theorem to write the first three terms of (2a+b)17.
Problem 46RE: Find the fourth term of (3a22b)11 without fully expanding the binomial.
Problem 47RE: For the following exercises, assume two die are rolled. 47. Construct a table showing the sample...
Problem 48RE: For the following exercises, assume two die are rolled. 48. What is the probability that a roll...
Problem 49RE: For the following exercises, assume two die are rolled. 49. What is the probability of rolling a...
Problem 50RE: For the following exercises, assume two die are rolled. 50. What is the probability that a roll...
Problem 51RE: For the following exercises, assume two die are rolled. 51.What is the probability that a roll...
Problem 52RE: For the following exercises, assume two die are rolled. 52. What is the probability of rolling a 5...
Problem 53RE: For the following exercises, assume two die are rolled. 53. What is the probability that a roll...
Problem 54RE: For the following exercises, use the following data: An elementary school survey found that 350 of...
Problem 55RE: For the following exercises, use the following data: An elementary school survey found that 350 of...
Problem 56RE: For the following exercises, use the following data: An elementary school survey found that 350 of...
Problem 57RE: For the following exercises, use the following data: An elementary school survey found that 350 of...
Problem 1PT: Write the first four terms of the sequence defined by the recursive formula a=14,an=2+an12
Problem 2PT: Write the first four terms of the sequence defined by the explicit formula an=n2n1n! .
Problem 3PT: Is the sequence 0.3,1.2,2.1,3,... arithmetic? If sofind the common difference.
Problem 4PT: An arithmetic sequence has the first term a1=4 and common difference d=43 .What is the 6thterm?
Problem 5PT: Write a recursive formula for the arithmetic sequence 2,72,5,132,... and then find the 22nd term.
Problem 6PT: Write an explicit formula for the arithmetic sequence 15.6,15,14.4,13.8,... and then find the 32...
Problem 7PT: Is the sequence 2,1,12,14,... . geometric? If sofind the common ratio. If not, explain why.
Problem 8PT: What is the 11thterm of the geometric sequence 1.5,3,6,12,... ?
Problem 9PT: Write a recursive formula for the geometric sequence 1,12,14,18,....
Problem 10PT: Write an explicit formula for the geometric sequence 4,43,49,427,....
Problem 11PT: Use summation notation to write the sum of terms 3k256k from k=3 to k=15 .
Problem 12PT: A community baseball stadium has 10 seats in the first row, 13 seats in the second row, 16 seats in...
Problem 13PT: Use the formula for the sum of the first n terms of a geometric series to find k=170.2(5)k1 .
Problem 14PT: Find the sum of the infinite geometric series. k=113(15)k1
Problem 15PT: Rachael deposits $3,600 into a retirement fund each year. The fund earns 7.5% annual interest,...
Problem 16PT: In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18...
Problem 17PT: A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3...
Problem 18PT: To allocate annual bonuses, a manager must choose his top four employees and rank them first to...
Problem 19PT: A rock group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can...
Problem 20PT: A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many...
Problem 21PT: How many distinct ways can the word EVANESCENCE be arranged if the anagram must end with the letter...
Problem 22PT: Use the Binomial Theorem to expand (32x12y)5 .
Problem 23PT: Find the seventh term of (x212)13 “without fully expanding the binomial.
Problem 24PT: For the following exercises, use the spinner in Figure 1. Figure 1 24. Construct a probability model...
Problem 25PT: For the following exercises, use the spinner in Figure 1. Figure 1 25. What is the probability of...
Problem 26PT: For the following exercises, use the spinner in Figure 1. Figure 1 26. What is the probability of...
Problem 27PT: For the following exercises, use the spinner in Figure 1. Figure 1 27. What is the probability of...
Problem 28PT: For the following exercises, use the spinner in Figure 1. Figure 1 28. What is the probability of...
Problem 29PT: For the following exercises, use the spinner in Figure 1. Figure 1 29. A bowl of candy holds 16...
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4(1). Find the Laurent series expansion for (22-1)(+2) in the annulus {1 < [z] <2}.
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