\(\frac{9}{2.5}+\frac{39}{5.8}+\frac{87}{8.11}+...+\frac{9897}{98.101}\)
\(=1-\frac{1}{2.5}+1-\frac{1}{5.8}+1-\frac{1}{8.11}+...+1-\frac{1}{98.101}\)
\(=1+1+...+1-\left(\frac{1}{2.5}+\frac{1}{5.8}+\frac{1}{8.11}+...+\frac{1}{98.101}\right)\) \(\left(\text{33 chữ số 1}\right)\)
\(=33-\frac{1}{3}\left(\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{98.101}\right)\)
\(=33-\frac{1}{3}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{98}-\frac{1}{101}\right)\)
\(=3-\frac{1}{3}\left(\frac{1}{2}-\frac{1}{101}\right)\)
\(=3-\frac{1}{3}-\frac{99}{202}\)
\(=\frac{1319}{606}\)
