Phạm Khắc Phương Nam
22 tháng 8 2019 lúc 21:49
\(\frac{1}{1\times2}\)+\(\frac{1}{2\times3}\)+\(\frac{1}{3\times4}\)+\(\frac{1}{4\times5}\)+\(\frac{1}{5\times6}\)+\(\frac{1}{6\times7}\)\(=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)\(=\left(\frac{1}{2}+\frac{1}{42}\right)+\left(\frac{1}{6}+\frac{1}{30}\right)+\left(\frac{1}{12}+\frac{1}{30}\right)\)\(=\frac{11}{21}+\frac{1}{5}+\frac{7}{60}\)\(=\frac{220}{420}+\frac{84}{420}+\frac{49}{420}\) \(=\frac{220+84+49}{420}=\frac{353}{420}\)