Find a specific geometric series which sums to 30
The series $\displaystyle \sum_{n=0}^\infty ar^n$ sums to $\displaystyle \frac{a}{1- r}$. Whether that is a rational number or an irrational number depends upon a and r. For example, given any rational number, u, take a= 1 and solve $\displaystyle \frac{1}{1- r}= u$. Given any irrational number, v, take a= v/2 and a= 1/2.