# Infinite geometric series problem

1. Jan 30, 2008

### sebastianbravom

1. The problem statement, all variables and given/known data

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

for what values of x does the series converge?

2. Relevant 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.

3. The attempt at a solution

2. Jan 30, 2008

### EnumaElish

3. Jan 30, 2008

### 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?

4. Jan 30, 2008

### 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.

5. Jan 30, 2008

### sutupidmath

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

6. Jan 30, 2008

### sebastianbravom

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