Let $S_n = (\sum_{k=1}^{n} a_k )^2$, where $a_k$ $=$ $( k * ( k + 2 ) )^{-1}$ . Let $S_n = ( p / q )$, where $p$ and $q$ are positive integers and $gcd( p , q ) = 1$ . Find the value of $p * q$ for $n = 112358$ .