2. Calculate: $\frac{1^{2}}{1^{2}-100+5000}+\frac{3^{2}}{3^{2}-300+5000}+$ $\frac{5^{2}}{5^{2}-500+5000}+\cdots+\frac{99^{2}}{99^{2}-9900+5000}=$ $\qquad$
2.50.

Notice that
$$
\begin{array}{l}
\frac{k^{2}}{k^{2}-100 k+5000}+\frac{\left(100-k^{2}\right)}{(100-k)^{2}-100(100-k)+5000} \\
=\frac{k^{2}}{k^{2}-100 k+5000}+\frac{10000-200 k+k^{2}}{k^{2}-100 k+5000} \\
=\frac{2\left(k^{2}-100 k+5000\right)}{k^{2}-100 k+5000}=2 .
\end{array}
$$

Let $k=1,3,5, \cdots, 49$, and add them up, we know the original expression $=2 \times 25=50$.