1/20+1/30+1/42+1/56+1/72+1/90+1/110+1/132
=1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10+1/10.11+1/11.12
=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/11-1/12
=1/4-1/12
=3/12-1/12
=1/6
= \(\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{11.12}\)
=\(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.....+\frac{1}{11}-\frac{1}{12}\)
=\(\frac{1}{4}-\frac{1}{12}\)
=\(\frac{1}{6}\)
\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)
\(=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}\)
\(=\frac{1}{4}+\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-\frac{1}{6}+\frac{1}{7}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{12}\)
\(=\frac{1}{4}-\frac{1}{12}\)
\(=\frac{1}{6}\)
