1/20 + 1/30 + 1/42 + ... + 1/156
= 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/12.13
= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/12 - 1/13
= 1/4 - 1/13
= 9/52
\(=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+....+\frac{1}{12}-\frac{1}{13}\)
\(=\frac{1}{4}-\frac{1}{13}=\frac{9}{52}\)
****
= 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 + 1/11.12 + 1/12.13
= 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/2 - 1/13
= 1/4 - 1/13
= 9/52
1/20+1/30+1/42+...+1/156
\(=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{12\cdot13}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{12}-\frac{1}{13}\)
\(=\left(\frac{1}{4}-\frac{1}{13}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)+...+\left(\frac{1}{12}-\frac{1}{12}\right)=\left(\frac{13}{52}-\frac{4}{52}\right)+0+...+0=\frac{9}{52}\)
\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+....+\frac{1}{156}\)
= \(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{12.13}\)
= \(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{12}-\frac{1}{13}\)
= \(\frac{1}{4}-\frac{1}{13}\)
= \(\frac{9}{52}\)
