\(42+\frac{93}{6}+\frac{87}{12}+\frac{79}{20}+\frac{69}{30}+\frac{57}{42}\)
\(=37+\left(1+\frac{93}{6}\right)+\left(1+\frac{87}{12}\right)+\left(\frac{79}{20}+1\right)+\left(1+\frac{69}{30}\right)+\left(1+\frac{57}{42}\right)\)
\(=37+\frac{99}{6}+\frac{99}{12}+\frac{99}{20}+\frac{99}{30}+\frac{99}{42}\)
\(=37+99\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=37+99\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(=37+99\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=37+99\left(\frac{1}{2}-\frac{1}{7}\right)\)
\(=37+99.\frac{5}{14}\)
\(=37+35\frac{5}{14}\)
\(=72\frac{5}{14}\)
