Here is the formula for $\displaystyle r$:

$\displaystyle r = \dfrac{a_{n+1}}{a_{n}}$ What would go in the numerator and denominator, in this case?

Anyhow since $\displaystyle \dfrac{1}{10} < 1$ then the geometric series does NOT diverge

But here is another question. Now, we have to find the sum. Is it possible that, after this point, the series could diverge?

$\displaystyle S = \dfrac{a}{1 - r}$

$\displaystyle S = \dfrac{\dfrac{3}{10}}{1 - \dfrac{1}{10}} = \dfrac{1}{3}$ - The infinite series converges. But what does this have to do with the sum?