Finding values of x where the infinite geometric series converge

[meeklobraca]

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!

 

[tiny-tim]

hmm …

(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!

Hint: does it converge for x = 0?

 

[gabbagabbahey]

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

 

[meeklobraca]

Hint: does it converge for x = 0?

No I don't think so?

Does your laughing faces mean I got it right? lol

 

[tiny-tim]

i need glasses

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.

Yes … sorry, meeklobraca … you got it right!