= 1/7.8 + 1/8.9 + 1/9.10 + 1/ 10.11 + 1/11.12 + 1/12.13
= 1/7 - 1/8 + 1/8 - 1/9 +......+1/12 - 1/13
= 1/7 - 1/13
= 6/91
\(S=\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}+\frac{1}{156}\)
\(S=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}\)
\(S=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{12}-\frac{1}{13}\)
\(S=\frac{1}{4}-\frac{1}{13}=\frac{9}{52}\)