Ta có: \(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)
\(=2.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2.\left(1-\frac{1}{20}\right)=\frac{2.19}{20}=\frac{19}{10}\)
\(\frac{2}{1\times2}+\frac{2}{2\times3}+......+\frac{2}{19\times20}\)
\(=2\left(\frac{1}{1\times2}+\frac{1}{2\times3}+.......+\frac{1}{19\times20}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+........+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\left(1-\frac{1}{20}\right)=2.\frac{19}{20}=\frac{19}{10}\)
\(\frac{2}{1\times2}+\frac{2}{2\times3}+....+\frac{2}{19\times20}\)
\(=2\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+....+\frac{1}{19\times20}\right)\)
\(=2\times\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\times\left(1-\frac{1}{20}\right)
=2\times\frac{19}{20}
=\frac{19}{10}\)
chúc bạn học tôt nha ^^