Question

Tính nhanh :  \(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{9\times10}\)

Answer 1

\(\frac{2}{1\times2}+\frac{2}{2\times3}+\frac{2}{3\times4}+...+\frac{2}{9\times10}\)

=\(2\times\frac{1}{1\times2}+2\times\frac{1}{2\times3}+2\times\frac{1}{3\times4}+...+2\times\frac{1}{9\times10}\)

=\(2\times\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{9\times10}\right)\)

=\(2\times\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)

=\(2\times\left(\frac{1}{1}-\frac{1}{10}\right)=2\times\left(\frac{10}{10}-\frac{1}{10}\right)=2\times\frac{9}{10}\)

=\(\frac{9}{5}\)

Answer 2

=2-1+1-\(\frac{2}{3}\)+\(\frac{2}{3}\)-\(\frac{1}{2}\)+...+\(\frac{2}{9}\)-\(\frac{1}{5}\)

=2-\(\frac{1}{5}\)

=\(\frac{10}{5}\)-\(\frac{1}{5}\)

=\(\frac{9}{5}\).

**** mình nha mấy bạn.