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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Determine whether the following series converges absolutely, converges conditionally or diverge
![The image contains two mathematical series expressions. They are as follows:
**(a) Series Expression:**
\[
\sum_{k=1}^{\infty} \left(\frac{3 - 2019k^2}{2020k^2 + 6}\right)^k
\]
This expression represents an infinite series starting from \(k=1\) to infinity. The general term of the series involves a fraction within an exponent, where the numerator is \(3 - 2019k^2\) and the denominator is \(2020k^2 + 6\).
**(b) Series Expression:**
\[
\sum_{k=1}^{\infty} (-2)^k \frac{(k!)^3}{(3k)!}
\]
This is another infinite series starting from \(k=1\) to infinity. The general term of this series involves the term \((-2)^k\) multiplied by the cube of \(k!\) (factorial of \(k\)) divided by the factorial of \(3k\).
These series may represent mathematical problems related to convergence or divergence, commonly analyzed in advanced calculus or mathematical analysis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0df6ed25-2bb9-4a04-818b-8faea1134696%2F080062be-cedc-4ee7-9678-20389cbf1d81%2Fptiliq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains two mathematical series expressions. They are as follows:
**(a) Series Expression:**
\[
\sum_{k=1}^{\infty} \left(\frac{3 - 2019k^2}{2020k^2 + 6}\right)^k
\]
This expression represents an infinite series starting from \(k=1\) to infinity. The general term of the series involves a fraction within an exponent, where the numerator is \(3 - 2019k^2\) and the denominator is \(2020k^2 + 6\).
**(b) Series Expression:**
\[
\sum_{k=1}^{\infty} (-2)^k \frac{(k!)^3}{(3k)!}
\]
This is another infinite series starting from \(k=1\) to infinity. The general term of this series involves the term \((-2)^k\) multiplied by the cube of \(k!\) (factorial of \(k\)) divided by the factorial of \(3k\).
These series may represent mathematical problems related to convergence or divergence, commonly analyzed in advanced calculus or mathematical analysis.
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