(1) $\lim \limits _{n \rightarrow \infty }\left [ \frac {1}{1 \times 2}+ \frac {1}{2 \times 3}+ \cdots + \frac {1}{n(n+1)}\right ]= \underline { \quad \quad \quad }$.

(2)$ \lim \limits _{n \rightarrow \infty } \left ( \dfrac {n}{n^{2}+1}+ \dfrac {n}{n^{2}+2}+ \cdots + \dfrac {n}{n^{2}+n} \right )= \underline { \quad \quad \quad }$.

(3) $\lim \limits _{n \rightarrow \infty } \left ( \frac {1}{n+1}+ \frac {1}{n+2}+ \cdots + \frac {1}{n+n} \right )= \underline { \quad \quad \quad }$.

(4) $\lim \limits _{n \rightarrow \infty } \sum \limits _{i=1}^{n} \dfrac {i}{n^{2}}e^{ \dfrac {i}{n}}= \underline { \quad \quad \quad }$.