$\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+...+\frac{1}{9800}=\frac{n+5^2}{200}$
$⇔\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}=\frac{n+25}{200}$
$⇔\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}=\frac{2.(n+25)}{200}$
$⇔\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}=\frac{n+25}{100}$
$⇔\frac{1}{2}-\frac{1}{100}=\frac{n+25}{100}$
$⇔\frac{49}{100}=\frac{n+25}{100}$
$⇔49=n+25$
$⇔n=24$
Vậy $n=24$.
