\(\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+\frac{2}{10\cdot13}+\frac{2}{13\cdot16}\)
\(=2\left(\frac{1}{4\cdot7}+\frac{1}{7\cdot10}+\frac{1}{10\cdot13}+\frac{1}{13\cdot16}\right)\)
\(=2\left[\frac{1}{3}\left(\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+\frac{3}{13\cdot16}\right)\right]\)
\(=2\left[\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\right]\)
\(=2\left[\frac{1}{3}\left(\frac{1}{4}-\frac{1}{16}\right)\right]\)
\(=2\left[\frac{1}{3}\cdot\frac{3}{16}\right]\)
\(=2\cdot\frac{1}{16}\)
\(=\frac{2}{16}=\frac{1}{8}\)
Ta có :
\(\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}\)
\(=\)\(2\left(\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+\frac{1}{13.16}\right)\)
\(=\)\(\frac{2}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\right)\)
\(=\)\(\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)
\(=\)\(\frac{2}{3}\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(=\)\(\frac{2}{3}.\frac{3}{16}\)
\(=\)\(\frac{1}{8}\)
Chúc bạn học tốt ~
\(\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}\)
= \(\frac{2}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}\right)\)
= \(\frac{2}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}\right)\)
= \(\frac{2}{3}\left(\frac{1}{4}-\frac{1}{16}\right)\)
= \(\frac{2}{3}.\frac{3}{16}\)
= \(\frac{1}{8}\)
