\(S=\frac{1}{3.6}+\frac{1}{6.9}+...+\frac{1}{219.222}\)
\(\Rightarrow3S=\frac{3}{3.6}+\frac{3}{6.9}+...+\frac{3}{219.222}\)
\(=\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{219}-\frac{1}{222}\)
\(=\frac{1}{3}-\frac{1}{222}< \frac{1}{3}\)
\(\Rightarrow S< \frac{1}{9}< 1\)
\(\Rightarrow S< 1\left(đpcm\right)\)