How to calculate infinite series?

[thecaptain90]

Hi, I'm stuck on a problem because I don't know how to calculate this series:
Ʃ(2^n * x^n), n starts from 0 to infinity. How can I calculate this? Do I have to transform it into something else where I know the outcome of the Σ like we do with the geometric functions?

 

[JJacquelin]

Hi, I'm stuck on a problem because I don't know how to calculate this series:
Ʃ(2^n * x^n), n starts from 0 to infinity. How can I calculate this? Do I have to transform it into something else where I know the outcome of the Σ like we do with the geometric functions?

Let X=2x
Ʃ(X^n) is the classical geometric series.

 

[thecaptain90]

Thanks, didn't think of doing this.

 

[Norfonz]

Be advised that |X| < 1 to treat this as a geometric series.