For what values of x(x≠0) will the following infinite geometric series have a finate sum?

Question

x+3x²+9x³+...

3x²/x
what are the next steps?

Thanks in advance.

Answer 1

The ratio of succesasive terms is 3x. This must be less than 1 for the infinite series to have a finite sum. Therefore x < 1/3 is required.

Answer 2

Thanks!