\(a.\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\)
\(=\frac{1}{2}-\frac{1}{5}\)
\(=\frac{3}{10}\)
\(b.\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}\)
\(=2\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}\right)\)
\(=2\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)\)
\(=2\cdot\left(\frac{1}{2}-\frac{1}{5}\right)\)
\(=2\cdot\frac{3}{10}=\frac{3}{5}\)
\(c.\frac{1}{2\cdot3}+\frac{2}{3\cdot5}+\frac{3}{5\cdot8}\)
\(=\frac{1}{6}+\frac{2}{15}+\frac{3}{40}\)
\(=\frac{3}{8}\)
k nha 500 AE
a, \(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}\)
\(=\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+\frac{5-4}{4\times5}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\)
\(=\frac{1}{2}-\frac{1}{5}\)
\(=\frac{3}{10}\)
b, \(\frac{2}{2\times3}+\frac{2}{3\times4}+\frac{2}{4\times5}\)
\(=\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+\frac{5-4}{4\times5}\)
\(=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)\times\frac{2}{1}\)
\(=\left(\frac{1}{2}-\frac{1}{5}\right)\times\frac{2}{1}\)
\(=\frac{3}{10}\times\frac{2}{1}\)
\(=\frac{3}{5}\)
c, \(\frac{1}{2\times3}+\frac{2}{3\times5}+\frac{3}{5\times8}\)
\(=\frac{3-2}{2\times3}+\frac{5-3}{3\times5}+\frac{8-5}{5\times8}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}\)
\(=\frac{1}{2}-\frac{1}{8}\)
\(=\frac{3}{8}\)
Bạn Nguyễn Đoàn Tâm chỉ đúng câu a và b thôi còn câu c sai rùi . sorry, mình nhìn nhầm
