Đặt A=1/10+1/15+1/21+...+1/120
1/2 A=1/20+1/30+1/42+...+1/240
A=1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16
A=1/4-1/16
A=3/16
Vậy:1/10+1/15+1/21+...+1/120=3/16
\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}=2\times\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(C=2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{15\times16}\right)\)
\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=2\times\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{3}{8}\)
\(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}=\frac{1}{2}x\left(\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}\right):\frac{1}{2}\)
= \(\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right):\frac{1}{2}=\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{15.16}\right):\frac{1}{2}\)
= \(\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right):\frac{1}{2}=\left(\frac{1}{4}-\frac{1}{16}\right):\frac{1}{2}=\frac{3}{8}\)
