\(giải:\)
\(S=\frac{2}{2.6}+\frac{2}{6.10}+...+\frac{2}{96.100}\)
\(\Rightarrow2S=2\left(\frac{2}{2.6}+\frac{2}{6.10}+...+\frac{2}{96.100}\right)\)
\(\Rightarrow2S=\frac{4}{2.6}+\frac{4}{6.10}+...+\frac{4}{96.100}\)
\(\Rightarrow2S=\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+...+\frac{1}{96}-\frac{1}{100}\)
\(2S=\frac{1}{2}-\frac{1}{100}\)
\(\Rightarrow S=\left(\frac{1}{2}-\frac{1}{100}\right):2\)
\(\Rightarrow S=\frac{49}{100}:2=\frac{49}{200}\)
VẬY S=49/100
\(=\frac{2}{4}\times\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+...+\frac{1}{96}-\frac{1}{100}\right)\)
\(=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{100}\right)\)
\(=\frac{1}{2}\times\frac{49}{100}=\frac{49}{200}\)