Question

Tính bằng cách nhanh nhất :

\(\frac{2}{1x2}\)+ \(\frac{2}{2x3}\)+ \(\frac{2}{3x4}\)+ ............... + \(\frac{2}{18x19}\)+ \(\frac{2}{19x20}\)

Giúp mik với nhé mik đang cần rất gấp .

Answer 1

Ta có: \(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{18.19}+\frac{2}{19.20}=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{18.19}+\frac{1}{19.20}\right)\)

      \(=2.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{18}-\frac{1}{19}+\frac{1}{19}-\frac{1}{20}\right)\)

       \(=2.\left(1-\frac{1}{20}\right)=\frac{2.19}{20}=\frac{19}{10}\)

Answer 2

\(\frac{2}{1\times2}+\frac{2}{2\times3}+......+\frac{2}{19\times20}\)

\(=2\left(\frac{1}{1\times2}+\frac{1}{2\times3}+.......+\frac{1}{19\times20}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+........+\frac{1}{19}-\frac{1}{20}\right)\)

\(=2\left(1-\frac{1}{20}\right)=2.\frac{19}{20}=\frac{19}{10}\)

Answer 3

\(\frac{2}{1\times2}+\frac{2}{2\times3}+....+\frac{2}{19\times20}\)
\(=2\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+....+\frac{1}{19\times20}\right)\)
\(=2\times\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{19}-\frac{1}{20}\right)\)
\(=2\times\left(1-\frac{1}{20}\right) =2\times\frac{19}{20} =\frac{19}{10}\)
chúc bạn học tôt nha ^^