Finding values of x where the infinite geometric series converge

Click For Summary

Homework Help Overview

The discussion revolves around determining the values of x for which an infinite geometric series converges, specifically the series represented by (2+x)+(2+x)^2+(2+x)^3 + ...

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the condition for convergence, noting that the common ratio is (2+x) and exploring the inequality -1 < 2 + x < 1. Questions arise regarding specific values of x, such as x = 0, and whether the initial interpretation of the convergence range is correct.

Discussion Status

Some participants express uncertainty about the correctness of the derived range for x, while others provide hints and affirmations. There is an acknowledgment of potential misreading of the inequality, but no clear consensus has been reached on the final interpretation.

Contextual Notes

Participants are navigating through the implications of the convergence criteria and are reflecting on their understanding of the series without providing definitive solutions.

meeklobraca
Messages
188
Reaction score
0

Homework Statement


(2+x)+(2+x)^2+(2+x)^3 + ...


Homework Equations







The Attempt at a Solution



Ive found that the l r l < 1

the r of this equation is (2 + x)

so we have -1 < 2 + x < 1

The values of x where the series coverges is -3 < x < -1

Is this correct?

Thanks!
 
Physics news on Phys.org
hmm …

meeklobraca said:
(2+x)+(2+x)^2+(2+x)^3 + ...
…
Ive found that the l r l < 1

the r of this equation is (2 + x)

so we have -1 < 2 + x < 1

The values of x where the series coverges is -3 < x < -1

Is this correct?

Thanks!

:smile: :smile: :smile: :smile:

Hint: does it converge for x = 0? :wink:
 
meeklobraca said:

Homework Statement


(2+x)+(2+x)^2+(2+x)^3 + ...


Homework Equations







The Attempt at a Solution



Ive found that the l r l < 1

the r of this equation is (2 + x)

so we have -1 < 2 + x < 1

The values of x where the series coverges is -3 < x < -1

Is this correct?

Thanks!

Looks good to me:approve:
 


tiny-tim said:
:smile: :smile: :smile: :smile:

Hint: does it converge for x = 0? :wink:



No I don't think so?

Does your laughing faces mean I got it right? lol
 
i need glasses

meeklobraca said:
No I don't think so?

Does your laughing faces mean I got it right? lol

oh dear … I read a -1 as a 1. :redface:

Yes … sorry, meeklobraca … you got it right! :biggrin:
 

Similar threads

Coupled pendulum-spring system
  • · Replies 3 ·
Replies
3
Views
1K
How to parametrize motion of a pendulum in terms of Cartesian coordinates?
  • · Replies 1 ·
Replies
1
Views
1K
RCL series circuit analysis: Damping Constant
  • · Replies 1 ·
Replies
1
Views
926
Help Calculating probability between 2 limits for the ground state
  • · Replies 28 ·
Replies
28
Views
2K
Magnetic Field of an infinite current-carrying wire at a point
  • · Replies 5 ·
Replies
5
Views
1K
Understanding the generic nature of linearity in Physics
  • · Replies 2 ·
Replies
2
Views
1K
Designing a speed bump given the maximum vertical wheel acceleration
  • · Replies 18 ·
Replies
18
Views
2K
How to show that these sequences are summable?
  • · Replies 1 ·
Replies
1
Views
2K
Find speed of CoM after collision between ball and "square structure"
  • · Replies 42 ·
2
Replies
42
Views
4K
Understanding a math step in solving Schrödinger's equation for single particle in a box
  • · Replies 8 ·
Replies
8
Views
1K