Explanation of Solution Given: 1.234567 = 1.234567567567... Result used: The geometric series >) `ar"-1 (or) a + ar + ar² + is convergent if n=1 |r| < 1 and its sum is -"-, where a is the first term and ris the common ratio of the series. Calculation: Rewrite the number and express 1.234567 as follows, 1.234567 = 1.234 + 0.000567 1.234 + (0.00 67+ 0.000000567+ ·· ·) = 1.234 + 106 567 567 +...) 10° 567 (1) 1.234567 = 1.234 + 103n n=2 567 is geometric series with first term of the series is a Here, 567 103n n=: 106 and common ratio is r = 103 Since |r| < 1 and the Result stated above, the geometric series 567 is 103n n=2 convergent.
Explanation of Solution Given: 1.234567 = 1.234567567567... Result used: The geometric series >) `ar"-1 (or) a + ar + ar² + is convergent if n=1 |r| < 1 and its sum is -"-, where a is the first term and ris the common ratio of the series. Calculation: Rewrite the number and express 1.234567 as follows, 1.234567 = 1.234 + 0.000567 1.234 + (0.00 67+ 0.000000567+ ·· ·) = 1.234 + 106 567 567 +...) 10° 567 (1) 1.234567 = 1.234 + 103n n=2 567 is geometric series with first term of the series is a Here, 567 103n n=: 106 and common ratio is r = 103 Since |r| < 1 and the Result stated above, the geometric series 567 is 103n n=2 convergent.
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...
Related questions
Question
100%
In the image attached, the geometric series I need to solve begins with "2" (n = 2). I'm not sure why it begins at 2, and not 1. Do you know why this series begins with 2? Let me know if you need more clarification!
Transcribed Image Text:Explanation of Solution
Given:
1.234567 = 1.234567567567...
Result used:
The geometric series >)
`ar"-1 (or) a + ar + ar² +
is convergent if
n=1
|r| < 1 and its sum is -"-, where a is the first term and ris the common
ratio of the series.
Calculation:
Rewrite the number and express 1.234567 as follows,
1.234567 = 1.234 + 0.000567
1.234 + (0.00
67+ 0.000000567+ ·· ·)
= 1.234 +
106
567
567
+...)
10°
567
(1)
1.234567 = 1.234 +
103n
n=2
567
is geometric series with first term of the series is a
Here,
567
103n
n=:
106
and common ratio is r =
103
Since |r| < 1 and the Result stated above, the geometric series
567
is
103n
n=2
convergent.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning