\(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{5}-\frac{1}{10}=\frac{1}{10}\)
Đặt biểu thức là A ta có
A=1/30 + 1/42 +1/56 +....+1/90
A=1/5.6 +1/6.7 +1/7.8 +......+1/9.10
A=1/5-1/6+1/6-1/7+1/7-1/8+.....+1/9-1/10
A=1/5-1/10
A=2/10 -1/10
A=1/10
vậy A=1/10
\(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{90}\)
\(=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{9.10}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{5}-\frac{1}{10}=\frac{2}{10}-\frac{1}{10}=\frac{1}{10}\)