\(A=\frac{6}{5.8}+\frac{6}{8.11}+....+\frac{6}{87.90}\)
\(A=2.\left(\frac{3}{5.8}+\frac{3}{8.11}+....+\frac{3}{87\cdot90}\right)\)
\(A=2.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+....+\frac{1}{87}-\frac{1}{90}\right)\)
\(A=2.\left(\frac{1}{5}-\frac{1}{90}\right)\)
\(A=2.\frac{1}{6}=\frac{1}{3}\)