$$
\begin{array}{l}
14 \cdot 31 \text { Find }\left[\frac{2+\sqrt{2}}{2}\right]+\left[\frac{3+\sqrt{3}}{3}\right]+\left[\frac{4+\sqrt{4}}{4}\right]+\cdots \\
+\left[\frac{1989+\sqrt{1989}}{1989}\right]+\left[\frac{1990+\sqrt{1990}}{1990}\right] .
\end{array}
$$
(1st "Hope Cup" Mathematics Competition, 1990)
［Solution］When $k>1$,
$$
\sqrt{k}1)$.
Thus the original expression $=1989$.

Note: There seems to be a typographical error in the original text, where it says $\sqrt{k}1)$. It might be intended to be $\sqrt{k}-1$ or $\sqrt{k}+1$. Please verify the original problem statement.