13. Given $f(x)=\frac{x^{2}}{x^{2}-100 x+5000}$, find the value of $f(1)+f(2)+\cdots+f(100)$.
$$
\begin{array}{l}
f(x)=\frac{x^{2}}{x^{2}-100 x+5000}=\frac{x^{2}}{(x-50)^{2}+2500} \\
\Rightarrow f(k)+f(100-k)=\frac{k^{2}+(100-k)^{2}}{(k-50)^{2}+2500}=\frac{2 k^{2}-200 k+10000}{(k-50)^{2}+2500}=2, \\
\text { Let } k=0,1, \cdots, 100, \text { and let } S=f(0)+f(1)+f(2)+\cdots+f(100),
\end{array}
$$

Then $2 S=2 \times 101 \Rightarrow S=101$. Therefore, $f(1)+f(2)+\cdots+f(100)=101$.