Infinite geometric series problem

[sebastianbravom]

Homework Statement

Consider the following infinite geometric series: 1 + (2x/3) + (2x/3)^2 + (2x/3)^3 + ...

for what values of x does the series converge?

Homework Equations

i don't know what converge means, i guessed it was for what vlaues does the geometric series is infinite but i am not sure.

The Attempt at a Solution

 

[EnumaElish]

Here is a link that you might find useful: http://en.wikipedia.org/wiki/Convergent_series

 

[sutupidmath]

well remember that in order for a geometric series to converge all its terms should be greater than -1 and smaller than 1? do u know what to do now?

 

[rcmango]

well, I'm going through this type of math, now there is a formula for geometric series, it is like this: (first term) / (1-r)

you always want to plug the first term in the top of the equation, in your case it looks like 1.

 

[sutupidmath]

well, I'm going through this type of math, now there is a formula for geometric series, it is like this: (first term) / (1-r)

you always want to plug the first term in the top of the equation, in your case it looks like 1.

Well, he is looking for something else, he just needs to find the interval of x for which the series converges.

 

[sebastianbravom]

thank you so much for that hint it really cleared everything! the web pages kept talking aobut limitations...i remebered now! thanks