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\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{4}-\frac{1}{10}=\frac{5}{20}-\frac{2}{20}=\frac{3}{20}\)
\(\frac{1}{20}\)+ \(\frac{1}{30}\)+ \(\frac{1}{42}\)+ \(\frac{1}{56}\)+ \(\frac{1}{72}\)+ \(\frac{1}{90}\)
= \(\frac{1}{4.5}\)+ \(\frac{1}{5.6}\)+ \(\frac{1}{6.7}\)+ \(\frac{1}{7.8}\)+ \(\frac{1}{8.9}\)+ \(\frac{1}{9.10}\)
= \(\frac{1}{4}\)- \(\frac{1}{5}\)+ \(\frac{1}{5}\)- \(\frac{1}{6}\)+ .... + \(\frac{1}{9}\)- \(\frac{1}{10}\)
= \(\frac{1}{4}\)- \(\frac{1}{10}\)
= \(\frac{5}{20}\)- \(\frac{2}{20}\)
= \(\frac{3}{20}\)
\(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\)
\(=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(=\frac{1}{4}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{6}-\frac{1}{6}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+\left(\frac{1}{8}-\frac{1}{8}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)-\frac{1}{10}\)
\(=\frac{1}{4}-\frac{1}{10}=\frac{3}{20}\)
~ Hok tốt ~