Sons and Daughters

In a strange town, there are n pairs of parents without any child, where n is a very large even number. The town is strange. When a daughter is born, they will stop making another baby. But when a son is born, they will make another baby. They will repeat it until a daughter is born.

Now the n pairs of parents start to make their babies. After few years, all of the n pairs of parents have their own daughters. Given that

P(a son is born) = P(a daughter is born)= $\frac{1}{2}$ ,

Find the value of $\frac{a}{b}$ , where a is the total number of sons of the n pairs of parents, b is the total number of daughters of the n pairs of parents.