làm cách thủ công đi
\(=\frac{20}{69}\)
\(\frac{4}{3.7}+\frac{5}{7.12}+\frac{1}{12.13}+\frac{7}{13.20}+\frac{3}{20.23}\)
=>\(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{23}\)
=> \(\frac{1}{3}-\frac{1}{23}\)=\(\frac{20}{69}\)
\(\frac{4}{3.7}+\frac{5}{7.12}+\frac{1}{12.13}+\frac{7}{13.20}+\frac{3}{20.23}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{23}\)
\(=\frac{1}{3}-\frac{1}{23}=\frac{20}{69}\)
\(\frac{4}{3\cdot7}+\frac{5}{7\cdot12}+\)\(\frac{1}{12\cdot13}+\)\(\frac{7}{13\cdot20}\)\(+\frac{3}{20\cdot23}\)
\(=\frac{1}{4\cdot7}+\frac{1}{7\cdot12}\)\(+\frac{1}{12\cdot13}\)\(+\frac{1}{13\cdot20}\)\(+\frac{1}{20\cdot23}\)
\(=\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}\)\(+\frac{1}{12}-\frac{1}{13}+\frac{1}{13}-\frac{1}{20}+\frac{1}{20}-\frac{1}{23}\)
\(=\frac{1}{4}-\frac{1}{23}\)
\(=\frac{19}{92}\)