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What is the expansion of the series Σ 3*+1? n=1 9+27+81 +243 9+12+15+18 3+9+27+81 3+6+9+12

What is the expansion of the series Σ 3*+1? n=1 9+27+81 +243 9+12+15+18 3+9+27+81 3+6+9+12

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question:** What is the expansion of the series \(\sum_{n=1}^{4} 3^{n+1}\)? **Options:** 1. \(9 + 27 + 81 + 243\) 2. \(9 + 12 + 15 + 18\) 3. \(3 + 9 + 27 + 81\) 4. \(3 + 6 + 9 + 12\) **Explanation:** To find the expansion of the series \(\sum_{n=1}^{4} 3^{n+1}\), evaluate each term of the series as follows: - For \(n = 1\): \(3^{1+1} = 3^2 = 9\) - For \(n = 2\): \(3^{2+1} = 3^3 = 27\) - For \(n = 3\): \(3^{3+1} = 3^4 = 81\) - For \(n = 4\): \(3^{4+1} = 3^5 = 243\) Thus, the series expands to \(9 + 27 + 81 + 243\), corresponding to option 1.
Transcribed Image Text:**Question:** What is the expansion of the series \(\sum_{n=1}^{4} 3^{n+1}\)? **Options:** 1. \(9 + 27 + 81 + 243\) 2. \(9 + 12 + 15 + 18\) 3. \(3 + 9 + 27 + 81\) 4. \(3 + 6 + 9 + 12\) **Explanation:** To find the expansion of the series \(\sum_{n=1}^{4} 3^{n+1}\), evaluate each term of the series as follows: - For \(n = 1\): \(3^{1+1} = 3^2 = 9\) - For \(n = 2\): \(3^{2+1} = 3^3 = 27\) - For \(n = 3\): \(3^{3+1} = 3^4 = 81\) - For \(n = 4\): \(3^{4+1} = 3^5 = 243\) Thus, the series expands to \(9 + 27 + 81 + 243\), corresponding to option 1.
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