Definite Integration

\(\mathop {\lim }\limits_{n\, \to \,\infty } \left( {{{{n^2}} \over {\left( {{n^2} + 1} \right)\left( {n + 1} \right)}} + {{{n^2}} \over {\left( {{n^2} + 4} \right)\left( {n + 2} \right)}} + {{{n^2}} \over {\left( {{n^2} + 9} \right)\left( {n + 3} \right)}} + ... + {{{n^2}} \over {\left( {{n^2} + {n^2}} \right)\left( {n + n} \right)}}} \right)\)

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