Determine the sum of the following infinite geometric series: 7 56 + 7++ M+... 64 56 40 O 80 64

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 the sum of the following infinite geometric series:**

\[ 56 + 7 + \frac{7}{8} + \frac{7}{64} + \ldots \]

**Options:**

- ○ 56
- ○ 40
- ○ 80
- ○ 64

This is an infinite geometric series where the first term \( a = 56 \) and the rest of the series starts at 7 with a common ratio \( r = \frac{1}{8} \).

To find the sum of this infinite geometric series starting from the second term, use the formula:

\[ S = \frac{a}{1 - r} \]

where \( a = 7 \) and \( r = \frac{1}{8} \). Add 56 to the sum obtained from the series.
Transcribed Image Text:**Determine the sum of the following infinite geometric series:** \[ 56 + 7 + \frac{7}{8} + \frac{7}{64} + \ldots \] **Options:** - ○ 56 - ○ 40 - ○ 80 - ○ 64 This is an infinite geometric series where the first term \( a = 56 \) and the rest of the series starts at 7 with a common ratio \( r = \frac{1}{8} \). To find the sum of this infinite geometric series starting from the second term, use the formula: \[ S = \frac{a}{1 - r} \] where \( a = 7 \) and \( r = \frac{1}{8} \). Add 56 to the sum obtained from the series.
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