Consider a $n\times n$ chess board. Let the total number of possible rectangles and squares be ${ R }_{ n }$ and ${ S }_{ n }$ respectively.

$\displaystyle{\lim _{ n\rightarrow \infty }{ \cfrac { { R }_{ n } }{ { n \ S }_{ n } } }}$

If the limit above is in the form of $\frac a b$ for coprime positive integers $a,b$, find $a+b$.

**Details and Assumptions**

- All squares are rectangles, but not all rectangles are squares.