Let's Play Chess on Other Planet

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.
Original
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