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
Solve these two questions pls

Transcribed Image Text:The image presents a mathematical problem involving an infinite series. The question asks for the sum of the series from n=1 to infinity of the expression \( \frac{8}{7^n} \). Four answer choices are provided:
- \( 7 \)
- \( \frac{4}{3} \)
- \( 1 \)
- \( \frac{28}{3} \)
To determine the correct answer, one needs to use the formula for the sum of an infinite geometric series, which is \( S = \frac{a}{1 - r} \), where \( a \) is the first term and \( r \) is the common ratio. In this series, \( a = \frac{8}{7} \) and \( r = \frac{1}{7} \).
![The image presents a mathematical expression that is part of a multiple-choice problem. The expression is an infinite series given by:
\[
\sum_{n=1}^{\infty} (-1)^{n-1} \frac{5}{4^n}
\]
Below the series, there are four possible answer options, listed as follows:
1. \(\frac{20}{3}\)
2. \(\frac{5}{3}\)
3. 1
4. 4
The task is to evaluate the series and select the correct result from the given options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F722c0934-aff7-4600-989e-1d198e6697ab%2F9398dcdb-beae-499e-8b61-0cb77598aec8%2Fik9kw0j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image presents a mathematical expression that is part of a multiple-choice problem. The expression is an infinite series given by:
\[
\sum_{n=1}^{\infty} (-1)^{n-1} \frac{5}{4^n}
\]
Below the series, there are four possible answer options, listed as follows:
1. \(\frac{20}{3}\)
2. \(\frac{5}{3}\)
3. 1
4. 4
The task is to evaluate the series and select the correct result from the given options.
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