Determine if each series converges or diverges and state which test justifies your conclusion. When appropriate, state if the series is absolutely convergent or conditionally convergent. 00 2n 4n? 00 Σ 1. n+1 2" n=1 n=1 1 4" 7. n=1 N+ \n+1 3" – 2 n=1 ¿ (2n)! (-1)" 8. n=0 Vn+5 00 Σ n° n=1 n+1 in' 4. E(-1)"e³ 9. 2n2 +1 n=0 n=1 -1)** n+1 Σ IT 5. n° +6 10. n=1 4 n=0 6. iM³ 2. 3.
Determine if each series converges or diverges and state which test justifies your conclusion. When appropriate, state if the series is absolutely convergent or conditionally convergent. 00 2n 4n? 00 Σ 1. n+1 2" n=1 n=1 1 4" 7. n=1 N+ \n+1 3" – 2 n=1 ¿ (2n)! (-1)" 8. n=0 Vn+5 00 Σ n° n=1 n+1 in' 4. E(-1)"e³ 9. 2n2 +1 n=0 n=1 -1)** n+1 Σ IT 5. n° +6 10. n=1 4 n=0 6. iM³ 2. 3.
Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
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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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![### Series Convergence and Divergence
Determine if each series converges or diverges and state which test justifies your conclusion. When appropriate, state if the series is **absolutely convergent** or **conditionally convergent**.
1. \[
\sum_{n=1}^{\infty} \left( \frac{2n}{n+1} \right)^n
\]
2. \[
\sum_{n=1}^{\infty} \frac{1}{n + \sqrt{n+1}}
\]
3. \[
\sum_{n=1}^{\infty} \frac{(2n)!}{n^5}
\]
4. \[
\sum_{n=0}^{\infty} (-1)^n e^{-2n}
\]
5. \[
\sum_{n=1}^{\infty} (-1)^{n+1} \frac{1}{n^3 + 6}
\]
6. \[
\sum_{n=1}^{\infty} \frac{4n^2}{2^n}
\]
7. \[
\sum_{n=1}^{\infty} \frac{4^n}{3^n - 2}
\]
8. \[
\sum_{n=0}^{\infty} \frac{(-1)^n}{\sqrt[3]{n+5}}
\]
9. \[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1} n^2}{2n^2 + 1}
\]
10. \[
\sum_{n=0}^{\infty} \left( \frac{\pi}{4} \right)^n
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf7f6c95-8471-427f-9da1-196effb3faf4%2F66c065da-95f4-4d57-a050-8d054b7f4512%2F6blv3ip.png&w=3840&q=75)
Transcribed Image Text:### Series Convergence and Divergence
Determine if each series converges or diverges and state which test justifies your conclusion. When appropriate, state if the series is **absolutely convergent** or **conditionally convergent**.
1. \[
\sum_{n=1}^{\infty} \left( \frac{2n}{n+1} \right)^n
\]
2. \[
\sum_{n=1}^{\infty} \frac{1}{n + \sqrt{n+1}}
\]
3. \[
\sum_{n=1}^{\infty} \frac{(2n)!}{n^5}
\]
4. \[
\sum_{n=0}^{\infty} (-1)^n e^{-2n}
\]
5. \[
\sum_{n=1}^{\infty} (-1)^{n+1} \frac{1}{n^3 + 6}
\]
6. \[
\sum_{n=1}^{\infty} \frac{4n^2}{2^n}
\]
7. \[
\sum_{n=1}^{\infty} \frac{4^n}{3^n - 2}
\]
8. \[
\sum_{n=0}^{\infty} \frac{(-1)^n}{\sqrt[3]{n+5}}
\]
9. \[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1} n^2}{2n^2 + 1}
\]
10. \[
\sum_{n=0}^{\infty} \left( \frac{\pi}{4} \right)^n
\]
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