$\begin{align}
& S=\frac{1}{2\times 5}+\frac{1}{5\times 8}+\frac{1}{8\times 11}+...+\frac{1}{97\times 100} \\
& S\times 3=\frac{3}{2\times 5}+\frac{3}{5\times 8}+\frac{3}{8\times 11}+...+\frac{3}{97\times 100} \\
& S\times 3=\frac{5-2}{2\times 5}+\frac{8-5}{5\times 8}+\frac{11-8}{8\times 11}+...+\frac{100-97}{97\times 100} \\
& S\times 3=\frac{5}{2\times 5}-\frac{2}{2\times 5}+\frac{8}{5\times 8}-\frac{5}{5\times 8}+\frac{11}{8\times 11}-\frac{8}{8\times 11}+...+\frac{100}{97\times 100}-\frac{97}{97\times 100} \\
& S\times 3=\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{97}-\frac{1}{100} \\
& S\times 3=\frac{1}{2}-\frac{1}{100}=\frac{49}{100} \\
& S=\frac{49}{100}:3=\frac{49}{300} \\
\end{align}$
Phân số thứ 2 con viết sai mẫu số nhé.