\(\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{n}{{{n^2}}} + \frac{n}{{{n^2} + {1^2}}} + \ldots \ldots \ldots .. + \frac{n}{{{n^2} + {{\left( {n - 1} \right)}^2}}}} \right]\)