1.(1) $\lim \limits _{m \rightarrow \infty } \sum \limits _{i=1}^{m} \sum \limits _{j=1}^{n} \dfrac {n}{(m+i)(n^{2}+j^{2})}= \underline { \quad \quad \quad }$.
(2) $\lim \limits _{n \rightarrow \infty } \sum \limits _{i=1}^{n} \sum \limits _{j=1}^{n} \dfrac {i}{n^{3}} \sin ^{2} \dfrac {2 \pi j}{n}= \underline { \quad \quad \quad }$.