Explanation Formula used: Sum of a Geometric Series: “If − 1 < r < 1 , the sum of the terms of an infinite geometric series with first term a 1 and common ratio r is ∑ n = 1 ∞ a 1 r n − 1 = a 1 1 − r ” Calculation: The given infinite geometric series is 6 − 2 + 2 3 − 2 9 + ⋯ . Since it is a geometric series, the first term a 1 is 6 and calculate the common ratio r as, − 2 6 = − 1 3 ( 2 3 ) ( − 2 ) = − 1 3 ( − 2 9 ) ( 2 3 ) = − 1 3 r = − 1 3 Note that, the common ratio r lies between −1 and 1

4th Edition

ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

See similar textbooks

Videos

Question

Chapter 13.3, Problem 53E

To determine

To find: The sum of the geometric series 6−2+23−29+⋯.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.3, Problem 52E

Chapter 13.3, Problem 54E

Students have asked these similar questions

In Problems 1–4, write down the first five terms of each sequence

In Problems 6–11, determine whether the given sequence is arithmetic,geometric, or neither. If the sequence is arithmetic, find thecommon difference and the sum of the first n terms. If the sequenceis geometric, find the common ratio and the sum of the first n terms

Often lottery winnings are divided into equal payments given annually for 20 – 25 years. So the present value of the winnings is worth less than the actual jackpot, depending on the rate at which money could be invested. Find the present value in dollars using the given conditions. Complete the table for each amount, interest rate, and number of payments. Jackpot Amount Interest Rate Equal Annual Payments Present Value (in dollars) $7,000,000 8% 20 $7,000,000 14% 20 $4 $7,000,000 8% 25 $ $7,000,000 14% 25 (Round to the nearest dollar as needed.)

Chapter 13 Solutions

Elementary & Intermediate Algebra

Ch. 13.1 - A(n) _____ is a function whose domain is the set...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Ch. 13.1 - Prob. 11E Ch. 13.1 - Prob. 12E Ch. 13.1 - Prob. 13E Ch. 13.1 - Prob. 14E Ch. 13.1 - Prob. 15E Ch. 13.1 - Prob. 16E Ch. 13.1 - Prob. 17E Ch. 13.1 - Prob. 18E Ch. 13.1 - Prob. 19E Ch. 13.1 - Prob. 20E Ch. 13.1 - Prob. 21E Ch. 13.1 - Prob. 22E Ch. 13.1 - Prob. 23E Ch. 13.1 - Prob. 24E Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.1 - Prob. 27E Ch. 13.1 - Prob. 28E Ch. 13.1 - Prob. 29E Ch. 13.1 - Prob. 30E Ch. 13.1 - Prob. 31E Ch. 13.1 - Prob. 32E Ch. 13.1 - Prob. 33E Ch. 13.1 - Prob. 34E Ch. 13.1 - Prob. 35E Ch. 13.1 - Prob. 36E Ch. 13.1 - Prob. 37E Ch. 13.1 - Prob. 38E Ch. 13.1 - Prob. 39E Ch. 13.1 - Prob. 40E Ch. 13.1 - Prob. 41E Ch. 13.1 - Prob. 42E Ch. 13.1 - Prob. 43E Ch. 13.1 - Prob. 44E Ch. 13.1 - Prob. 45E Ch. 13.1 - Prob. 46E Ch. 13.1 - Prob. 47E Ch. 13.1 - Prob. 48E Ch. 13.1 - Prob. 49E Ch. 13.1 - Prob. 50E Ch. 13.1 - Prob. 51E Ch. 13.1 - Prob. 52E Ch. 13.1 - Prob. 53E Ch. 13.1 - Prob. 54E Ch. 13.1 - Prob. 55E Ch. 13.1 - Population Growth According to the United States...Ch. 13.1 - Prob. 57E Ch. 13.1 - Prob. 58E Ch. 13.1 - Prob. 59E Ch. 13.1 - Prob. 60E Ch. 13.1 - Prob. 61E Ch. 13.1 - In Problems 5962, a sequence is defined...Ch. 13.1 - Prob. 63E Ch. 13.1 - Prob. 65E Ch. 13.1 - Prob. 66E Ch. 13.1 - Prob. 67E Ch. 13.1 - Prob. 68E Ch. 13.1 - Prob. 69E Ch. 13.1 - Prob. 70E Ch. 13.1 - Prob. 71E Ch. 13.1 - Prob. 72E Ch. 13.1 - Prob. 73E Ch. 13.1 - Prob. 74E Ch. 13.1 - Prob. 75E Ch. 13.1 - Prob. 76E Ch. 13.1 - Prob. 77E Ch. 13.1 - Prob. 78E Ch. 13.1 - Prob. 79E Ch. 13.1 - Prob. 80E Ch. 13.1 - Prob. 81E Ch. 13.1 - Prob. 82E Ch. 13.1 - Prob. 83E Ch. 13.1 - Prob. 84E Ch. 13.1 - Prob. 85E Ch. 13.1 - Prob. 86E Ch. 13.1 - Prob. 87E Ch. 13.1 - Use technology to find the sum. k=18[(1)kk]Ch. 13.2 - In a(n) _______ sequence, the difference between...Ch. 13.2 - Prob. 2E Ch. 13.2 - Prob. 3E Ch. 13.2 - Prob. 4E Ch. 13.2 - Prob. 5E Ch. 13.2 - Prob. 6E Ch. 13.2 - Prob. 7E Ch. 13.2 - Prob. 8E Ch. 13.2 - Prob. 9E Ch. 13.2 - Prob. 10E Ch. 13.2 - Prob. 11E Ch. 13.2 - Prob. 12E Ch. 13.2 - Prob. 13E Ch. 13.2 - Prob. 14E Ch. 13.2 - Prob. 15E Ch. 13.2 - Prob. 16E Ch. 13.2 - Prob. 17E Ch. 13.2 - Prob. 18E Ch. 13.2 - Prob. 19E Ch. 13.2 - Prob. 20E Ch. 13.2 - Prob. 21E Ch. 13.2 - Prob. 22E Ch. 13.2 - Prob. 23E Ch. 13.2 - Prob. 24E Ch. 13.2 - Prob. 25E Ch. 13.2 - Prob. 26E Ch. 13.2 - Prob. 27E Ch. 13.2 - Prob. 28E Ch. 13.2 - Prob. 29E Ch. 13.2 - Prob. 30E Ch. 13.2 - Prob. 31E Ch. 13.2 - Prob. 32E Ch. 13.2 - Prob. 33E Ch. 13.2 - Prob. 34E Ch. 13.2 - Prob. 35E Ch. 13.2 - Prob. 36E Ch. 13.2 - Prob. 37E Ch. 13.2 - Prob. 38E Ch. 13.2 - Prob. 39E Ch. 13.2 - Prob. 40E Ch. 13.2 - Prob. 41E Ch. 13.2 - Prob. 42E Ch. 13.2 - Prob. 43E Ch. 13.2 - Prob. 44E Ch. 13.2 - Prob. 45E Ch. 13.2 - Prob. 46E Ch. 13.2 - Prob. 47E Ch. 13.2 - Find the sum of the first 75 terms of the sequence...Ch. 13.2 - Prob. 49E Ch. 13.2 - Prob. 50E Ch. 13.2 - Prob. 51E Ch. 13.2 - Prob. 52E Ch. 13.2 - Prob. 53E Ch. 13.2 - Prob. 54E Ch. 13.2 - Prob. 55E Ch. 13.2 - Prob. 56E Ch. 13.2 - Prob. 57E Ch. 13.2 - Prob. 58E Ch. 13.2 - Prob. 59E Ch. 13.2 - Prob. 60E Ch. 13.2 - Prob. 61E Ch. 13.2 - Prob. 62E Ch. 13.2 - Prob. 63E Ch. 13.2 - Prob. 64E Ch. 13.2 - Prob. 65E Ch. 13.2 - Prob. 66E Ch. 13.2 - Prob. 67E Ch. 13.2 - Prob. 68E Ch. 13.2 - Prob. 69E Ch. 13.2 - Prob. 70E Ch. 13.2 - Prob. 71E Ch. 13.2 - Prob. 72E Ch. 13.2 - Prob. 73E Ch. 13.2 - Compute f(2)f(1), f(3)f(2), and f(4)f(3) for each...Ch. 13.2 - In Problems 75-78, use technology to find the sum...Ch. 13.2 - Prob. 76E Ch. 13.2 - Prob. 77E Ch. 13.2 - In Problems 75-78, use technology to find the sum...Ch. 13.3 - In a(n) __ sequence, the difference between...Ch. 13.3 - Prob. 2E Ch. 13.3 - Prob. 3E Ch. 13.3 - Prob. 4E Ch. 13.3 - Prob. 5E Ch. 13.3 - In Problems 5-7, determine whether the sequence is...Ch. 13.3 - Prob. 7E Ch. 13.3 - Prob. 8E Ch. 13.3 - Prob. 9E Ch. 13.3 - Prob. 10E Ch. 13.3 - Prob. 11E Ch. 13.3 - Prob. 12E Ch. 13.3 - Prob. 13E Ch. 13.3 - Prob. 14E Ch. 13.3 - Prob. 15E Ch. 13.3 - Express 0.2 as a fraction in lowest terms.Ch. 13.3 - Redo Example 9 if the marginal propensity to...Ch. 13.3 - Prob. 18E Ch. 13.3 - Prob. 19E Ch. 13.3 - Prob. 20E Ch. 13.3 - Prob. 21E Ch. 13.3 - Prob. 22E Ch. 13.3 - Prob. 23E Ch. 13.3 - Prob. 24E Ch. 13.3 - Prob. 25E Ch. 13.3 - Prob. 26E Ch. 13.3 - Prob. 27E Ch. 13.3 - Prob. 28E Ch. 13.3 - Prob. 29E Ch. 13.3 - Prob. 30E Ch. 13.3 - Prob. 31E Ch. 13.3 - Prob. 32E Ch. 13.3 - Prob. 33E Ch. 13.3 - Prob. 34E Ch. 13.3 - Prob. 35E Ch. 13.3 - Prob. 36E Ch. 13.3 - Prob. 37E Ch. 13.3 - In Problems 3540, find the indicated term of each...Ch. 13.3 - Prob. 39E Ch. 13.3 - Prob. 40E Ch. 13.3 - Prob. 41E Ch. 13.3 - Prob. 42E Ch. 13.3 - Prob. 43E Ch. 13.3 - Prob. 44E Ch. 13.3 - Prob. 45E Ch. 13.3 - Prob. 46E Ch. 13.3 - Prob. 47E Ch. 13.3 - Prob. 48E Ch. 13.3 - Prob. 49E Ch. 13.3 - Prob. 50E Ch. 13.3 - Prob. 51E Ch. 13.3 - Prob. 52E Ch. 13.3 - Prob. 53E Ch. 13.3 - Prob. 54E Ch. 13.3 - Prob. 55E Ch. 13.3 - Prob. 56E Ch. 13.3 - Prob. 57E Ch. 13.3 - Prob. 58E Ch. 13.3 - Prob. 59E Ch. 13.3 - Prob. 60E Ch. 13.3 - Prob. 61E Ch. 13.3 - Prob. 62E Ch. 13.3 - Prob. 63E Ch. 13.3 - Prob. 64E Ch. 13.3 - Prob. 65E Ch. 13.3 - Prob. 66E Ch. 13.3 - Prob. 67E Ch. 13.3 - Prob. 68E Ch. 13.3 - Prob. 69E Ch. 13.3 - Prob. 70E Ch. 13.3 - Prob. 71E Ch. 13.3 - Prob. 72E Ch. 13.3 - Prob. 73E Ch. 13.3 - Prob. 74E Ch. 13.3 - Prob. 75E Ch. 13.3 - Prob. 76E Ch. 13.3 - Prob. 77E Ch. 13.3 - Prob. 78E Ch. 13.3 - Prob. 79E Ch. 13.3 - Prob. 80E Ch. 13.3 - Prob. 81E Ch. 13.3 - Bouncing Balls A ball is dropped from a height of...Ch. 13.3 - Prob. 83E Ch. 13.3 - Prob. 84E Ch. 13.3 - Prob. 85E Ch. 13.3 - Prob. 86E Ch. 13.3 - Prob. 87E Ch. 13.3 - Prob. 88E Ch. 13.3 - Prob. 89E Ch. 13.3 - Prob. 90E Ch. 13.3 - Prob. 91E Ch. 13.3 - Prob. 92E Ch. 13.3 - Prob. 93E Ch. 13.3 - Prob. 94E Ch. 13.3 - Prob. 95E Ch. 13.3 - Prob. 96E Ch. 13.3 - Prob. 97E Ch. 13.3 - Prob. 98E Ch. 13.3 - Prob. 100E Ch. 13.3 - Prob. 101E Ch. 13.3 - Prob. 102E Ch. 13.3 - What is 13+23? Now add the repeating decimals...Ch. 13.3 - Prob. 104E Ch. 13.3 - Prob. 105E Ch. 13.3 - Prob. 106E Ch. 13.3 - Prob. 107E Ch. 13.3 - Prob. 108E Ch. 13.4 - If n 2 is an integer, then n! =...Ch. 13.4 - Prob. 2E Ch. 13.4 - Prob. 3E Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Prob. 6E Ch. 13.4 - Prob. 7E Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - Prob. 10E Ch. 13.4 - In Problems 11-18, evalute each factorial...Ch. 13.4 - Prob. 12E Ch. 13.4 - Prob. 13E Ch. 13.4 - Prob. 14E Ch. 13.4 - Prob. 15E Ch. 13.4 - Prob. 16E Ch. 13.4 - Prob. 17E Ch. 13.4 - Prob. 18E Ch. 13.4 - Prob. 19E Ch. 13.4 - Prob. 20E Ch. 13.4 - Prob. 21E Ch. 13.4 - Prob. 22E Ch. 13.4 - Prob. 23E Ch. 13.4 - Prob. 24E Ch. 13.4 - Prob. 25E Ch. 13.4 - Prob. 26E Ch. 13.4 - Prob. 27E Ch. 13.4 - Prob. 28E Ch. 13.4 - Prob. 29E Ch. 13.4 - In Problems 23-38, expand each expression using...Ch. 13.4 - Prob. 31E Ch. 13.4 - Prob. 32E Ch. 13.4 - Prob. 33E Ch. 13.4 - Prob. 34E Ch. 13.4 - Prob. 35E Ch. 13.4 - Prob. 36E Ch. 13.4 - Prob. 37E Ch. 13.4 - Prob. 38E Ch. 13.4 - Prob. 39E Ch. 13.4 - Prob. 40E Ch. 13.4 - Prob. 41E Ch. 13.4 - Prob. 42E Ch. 13.4 - Prob. 43E Ch. 13.4 - Prob. 44E Ch. 13.4 - Prob. 45E Ch. 13.4 - Prob. 46E Ch. 13.4 - Prob. 47E Ch. 13.4 - Prob. 48E Ch. 13.4 - Prob. 49E Ch. 13.4 - Prob. 50E Ch. 13.4 - Prob. 51E Ch. 13.4 - Prob. 52E Ch. 13.4 - Prob. 53E Ch. 13.4 - Prob. 54E Ch. 13.4 - Prob. 55E Ch. 13.4 - If h(x) = 2x5 + 5x4, find h(a + 3) with the aid of...Ch. 13 - In Problems 16, determine if the sequence is...Ch. 13 - Prob. 2PCT Ch. 13 - Prob. 3PCT Ch. 13 - Prob. 4PCT Ch. 13 - Prob. 5PCT Ch. 13 - Prob. 6PCT Ch. 13 - Prob. 7PCT Ch. 13 - Prob. 8PCT Ch. 13 - Prob. 9PCT Ch. 13 - Prob. 10PCT Ch. 13 - Prob. 11PCT Ch. 13 - Prob. 12PCT Ch. 13 - In problem 1315, find the indicated sum. 13....Ch. 13 - Prob. 14PCT Ch. 13 - Prob. 15PCT Ch. 13 - Prob. 16PCT Ch. 13 - Prob. 1RE Ch. 13 - Prob. 2RE Ch. 13 - Prob. 3RE Ch. 13 - Prob. 4RE Ch. 13 - Prob. 5RE Ch. 13 - Prob. 6RE Ch. 13 - Prob. 7RE Ch. 13 - Prob. 8RE Ch. 13 - Prob. 9RE Ch. 13 - Prob. 10RE Ch. 13 - Prob. 11RE Ch. 13 - Prob. 12RE Ch. 13 - Prob. 13RE Ch. 13 - Prob. 14RE Ch. 13 - Prob. 15RE Ch. 13 - Prob. 16RE Ch. 13 - Prob. 17RE Ch. 13 - Prob. 18RE Ch. 13 - Prob. 19RE Ch. 13 - Prob. 20RE Ch. 13 - Prob. 21RE Ch. 13 - Prob. 22RE Ch. 13 - Prob. 23RE Ch. 13 - Prob. 24RE Ch. 13 - Prob. 25RE Ch. 13 - Prob. 26RE Ch. 13 - Prob. 27RE Ch. 13 - Prob. 28RE Ch. 13 - Prob. 29RE Ch. 13 - Prob. 30RE Ch. 13 - Prob. 31RE Ch. 13 - Prob. 32RE Ch. 13 - Prob. 33RE Ch. 13 - Prob. 34RE Ch. 13 - Prob. 35RE Ch. 13 - Prob. 36RE Ch. 13 - Prob. 37RE Ch. 13 - Prob. 38RE Ch. 13 - Prob. 39RE Ch. 13 - Prob. 40RE Ch. 13 - Prob. 41RE Ch. 13 - Prob. 42RE Ch. 13 - Prob. 43RE Ch. 13 - Prob. 44RE Ch. 13 - Prob. 45RE Ch. 13 - Prob. 46RE Ch. 13 - Prob. 47RE Ch. 13 - Prob. 48RE Ch. 13 - Prob. 49RE Ch. 13 - Prob. 50RE Ch. 13 - Prob. 51RE Ch. 13 - Prob. 52RE Ch. 13 - Prob. 53RE Ch. 13 - Prob. 54RE Ch. 13 - Prob. 55RE Ch. 13 - In Problems 5356, find the sum of each geometric...Ch. 13 - Prob. 57RE Ch. 13 - Prob. 58RE Ch. 13 - Prob. 59RE Ch. 13 - Prob. 60RE Ch. 13 - Prob. 61RE Ch. 13 - Prob. 62RE Ch. 13 - Prob. 63RE Ch. 13 - Prob. 64RE Ch. 13 - Prob. 65RE Ch. 13 - Prob. 66RE Ch. 13 - Prob. 67RE Ch. 13 - Prob. 68RE Ch. 13 - Prob. 69RE Ch. 13 - Prob. 70RE Ch. 13 - Prob. 71RE Ch. 13 - Prob. 72RE Ch. 13 - Prob. 73RE Ch. 13 - Prob. 74RE Ch. 13 - Prob. 75RE Ch. 13 - Prob. 76RE Ch. 13 - Prob. 77RE Ch. 13 - Prob. 78RE Ch. 13 - Prob. 1T Ch. 13 - In Problems 16, determine whether the sequence is...Ch. 13 - Prob. 3T Ch. 13 - Prob. 4T Ch. 13 - Prob. 5T Ch. 13 - Prob. 6T Ch. 13 - Prob. 7T Ch. 13 - Prob. 8T Ch. 13 - Prob. 9T Ch. 13 - In Problems 912, write a formula for the nth term...Ch. 13 - Prob. 11T Ch. 13 - Prob. 12T Ch. 13 - Prob. 13T Ch. 13 - Prob. 14T Ch. 13 - Prob. 15T Ch. 13 - Prob. 16T Ch. 13 - Prob. 17T Ch. 13 - Prob. 18T Ch. 13 - Prob. 19T Ch. 13 - Prob. 20T Ch. 13 - Prob. 1CUR Ch. 13 - Prob. 2CUR Ch. 13 - Prob. 3CUR Ch. 13 - Prob. 4CUR Ch. 13 - Prob. 5CUR Ch. 13 - Prob. 6CUR Ch. 13 - Prob. 7CUR Ch. 13 - Prob. 8CUR Ch. 13 - Prob. 9CUR Ch. 13 - Prob. 10CUR Ch. 13 - Prob. 11CUR Ch. 13 - Prob. 12CUR Ch. 13 - Prob. 13CUR Ch. 13 - Prob. 14CUR Ch. 13 - Prob. 15CUR Ch. 13 - Prob. 16CUR Ch. 13 - Prob. 17CUR Ch. 13 - Prob. 18CUR Ch. 13 - Prob. 19CUR Ch. 13 - Prob. 20CUR Ch. 13 - Prob. 21CUR Ch. 13 - Prob. 22CUR Ch. 13 - Prob. 23CUR Ch. 13 - Prob. 24CUR Ch. 13 - Prob. 25CUR

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The sum of the geometric series 6 − 2 + 2 3 − 2 9 + ⋯ .

Solution Summary: The author explains the formula used to find the sum of a geometric series.

Videos

To find: The sum of the geometric series 6−2+23−29+⋯.

Want to see the full answer?

Chapter 13 Solutions