\(S=\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{20.22}\)
\(2S=\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{20.22}\)
\(2S=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{20}-\frac{1}{22}\)
\(2S=1-\frac{1}{22}=\frac{21}{22}\)
\(S=\frac{21}{22}:2=\frac{21}{44}\)