/sci/ - Science & Math

[math]f(x)=2x + 2x^2 + 2x^3 + ...[/math]
How to solve it? I know it's an infinite sum [math]\sum_{n=1}^{\infty} 2x^n [/math]
Or a geometric series [math]f(x)=a_n \Leftrightarrow a_n=2x^n\Leftrightarrow r=x[/math]
But I don't know how to solve it. I know that the sum of first n terms of a geometric series is [math]a_1\cdot\frac{1-r^n}{1-r}[/math], for [math] r\neq1[/math]
But in my case [math]r=x[/math], so how do I know if it's convergent or divergent?
I also found the formula for sum of geometric series [math]S_\infty=\frac{a1}{1−r}[/math], for [math]|r|<1[/math]
But again, in my case [math]r=x[/math], so I don't know if it fulfills that requirement.
The task is to draw that function.