So I was given the triangular array of numbers below (the first line consists of two "1")
$11$
$1\frac{3}{2}1$
$1\frac{6}{4}\frac{6}{4}1$
$1\frac{10}{7}\frac{10}{6}\frac{10}{7}1$
$1\frac{15}{11}\frac{15}{9}\frac{15}{9}\frac{15}{11}1$
and I was told to find a function of two variables $f(r,c)$ that takes as input the row number $r$ (starting with $1$) and the column number $c$ (starting with $0$) and outputs the correct number. So for example $f(3,1)=\frac{6}{4}$. The general statement is
$f(r,c)=\frac{r(r+1)}{(r-c)(r-c+1)+c(c+1)}$
My question is, how can I figure out if this triangle of numbers contains all rational numbers somewhere and if not, how do I figure out which fractions will never appear in this pattern?