Explanation Theorem Used: The general term of the first order linear difference equation with constant coefficients s n = a s n − 1 + b that has initial value s 0 satisfies s n = { a n ( s 0 + c ) − c if a ≠ 1 s 0 + n b if a = 1 where c = b a − 1 . Calculation: Consider s n = s 0 + s 0 r + s 0 r 2 + ⋯ + s 0 r n . Substitute n = 0 in s n = s 0 + s 0 r + s 0 r 2 + ⋯ + s 0 r n to get, s 0 = s 0 Substitute n = 1 in s n = s 0 + s 0 r + s 0 r 2 + ⋯ + s 0 r n to get, s 1 = s 0 + s 0 r Substitute n = 2 in s n = s 0 + s 0 r + s 0 r 2 + ⋯ + s 0 r n to get, s 2 = s 0 + s 0 r + s 0 r 2 = s 0 + r ( s 0 + s 0 r ) = s 0 + r s 1 Substitute n = 3 in s n = s 0 + s 0 r + s</

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ISBN: 9780134689562

Author: Dossey, John A.

Publisher: Pearson,

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Chapter 9.3, Problem 34E

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To find: formula for the sum of the first n+1 terms of a geometric progression with first term s₀ and common ratio r≠1.

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Chapter 9.3, Problem 33E

Chapter 9.3, Problem 35E

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Chapter 9 Solutions

Discrete Mathematics

Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Suppose that you have an unlimited supply of red,...Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.2 - Prove by mathematical induction that n2 − n + 2 is...Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prove by mathematical induction that is a...Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - Prob. 12E Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - Prob. 15E Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - In Exercises 11–24, use the method of iteration to...Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Prob. 26E Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Consider the sequences of n terms in which each...Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Prob. 33E Ch. 9.2 - Prob. 34E Ch. 9.3 - In Exercises 1–24, find an explicit formula for sn...Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - Prob. 9E Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Prob. 34E Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Prob. 37E Ch. 9.3 - Prob. 38E Ch. 9.4 - Prob. 1E Ch. 9.4 - Prob. 2E Ch. 9.4 - Prob. 3E Ch. 9.4 - Prob. 4E Ch. 9.4 - Prob. 5E Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - Prob. 9E Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - Prob. 12E Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - Prob. 17E Ch. 9.4 - Prob. 18E Ch. 9.4 - Prob. 19E Ch. 9.4 - Prob. 20E Ch. 9.4 - Prob. 22E Ch. 9.4 - Prob. 24E Ch. 9.4 - Prob. 26E Ch. 9.4 - Prob. 30E Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 34E Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 38E Ch. 9.5 - Prob. 1E Ch. 9.5 - Prob. 2E Ch. 9.5 - Prob. 3E Ch. 9.5 - Prob. 4E Ch. 9.5 - Prob. 5E Ch. 9.5 - Prob. 6E Ch. 9.5 - 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Prob. 23E Ch. 9.6 - Prob. 24E Ch. 9.6 - Prob. 25E Ch. 9.6 - Prob. 26E Ch. 9.6 - Prob. 27E Ch. 9.6 - Prob. 28E Ch. 9.6 - Prob. 29E Ch. 9.6 - Prob. 30E Ch. 9.6 - Prob. 31E Ch. 9.6 - Prob. 32E Ch. 9.6 - Prob. 34E Ch. 9.6 - Prob. 35E Ch. 9.6 - Prob. 36E Ch. 9.6 - Prob. 37E Ch. 9.6 - Prob. 38E Ch. 9.6 - Prob. 39E Ch. 9.6 - Prob. 40E Ch. 9.6 - Prob. 41E Ch. 9.6 - Prob. 42E Ch. 9 - Prob. 1SE Ch. 9 - Prob. 2SE Ch. 9 - Prob. 3SE Ch. 9 - Prob. 4SE Ch. 9 - Prob. 6SE Ch. 9 - A data processing position pays a starting salary...Ch. 9 - Prob. 8SE Ch. 9 - Prob. 9SE Ch. 9 - Prob. 10SE Ch. 9 - Prob. 11SE Ch. 9 - Prob. 12SE Ch. 9 - Prob. 13SE Ch. 9 - Prob. 14SE Ch. 9 - Prob. 17SE Ch. 9 - Prob. 18SE Ch. 9 - Prob. 19SE Ch. 9 - Prob. 21SE Ch. 9 - Prob. 22SE Ch. 9 - Prob. 23SE Ch. 9 - Prob. 41SE Ch. 9 - Prob. 42SE Ch. 9 - Prob. 43SE Ch. 9 - Prob. 44SE Ch. 9 - Prob. 45SE Ch. 9 - Prob. 46SE Ch. 9 - Prob. 47SE Ch. 9 - Prob. 48SE

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formula for the sum of the first n + 1 terms of a geometric progression with first term s 0 and common ratio r ≠ 1.

To find: formula for the sum of the first n+1 terms of a geometric progression with first term s0 and common ratio r≠1.

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Chapter 9 Solutions

To find: formula for the sum of the first n+1 terms of a geometric progression with first term s₀ and common ratio r≠1.