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! Explanation of SolutionGiven:1.234567 = 1.234567567567...Result used:The geometric series >)`ar"-1 (or) a + ar + ar² +is convergent ifn=1|r| < 1 and its sum is -"-, where a is the first term and ris the commonratio of the series.Calculation:Rewrite the number and express 1.234567 as follows,1.234567 = 1.234 + 0.0005671.234 + (0.0067+ 0.000000567+ ·· ·)= 1.234 +106567567+...)10°567(1)1.234567 = 1.234 +103nn=2567is geometric series with first term of the series is aHere,567103nn=:106and common ratio is r =103Since |r| < 1 and the Result stated above, the geometric series567is103nn=2convergent.

Answered: Image /qna-images/answer/9189909e-6be7-457c-9265-2a28e23b4b1f.jpg

Answered: Explanation of Solution Given: 1.234567…

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...

See similar textbooks

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!

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Series$

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.

Similar questions