Question 5
A boy has a cup of tea and a girl has an empty glass having the same volume as the cup. In the first step, the boy pours $\frac12$ of the tea from the cup into the glass. In the second step, the girl pours $\frac13$ of the tea from the glass into the cup. In the third step, the boy pours $\frac14$ of the tea from the cup into the glass. In the fourth step, the girl pours $\frac15$ of the tea from the glass into the cup. This alternate pouring continues such that in each step, the denominator increases by $1$. What fraction of the tea is in the cup after the thirteenth step?