Ta có : \(\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+....+\dfrac{1}{10}\right)\times x=\dfrac{1}{9}+\dfrac{2}{8}+....+\dfrac{8}{2}+\dfrac{9}{1}\)
Đặt \(A=\dfrac{1}{9}+\dfrac{2}{8}+....+\dfrac{8}{2}+\dfrac{9}{1}\)
\(=\left(9-1-1-....-1\right)+\left(\dfrac{8}{2}+1\right)+\left(\dfrac{7}{3}+1\right)+.....+\left(\dfrac{1}{9}+1\right)\)
\(=1+\dfrac{10}{2}+\dfrac{10}{3}+...+\dfrac{10}{9}=\dfrac{10}{2}+\dfrac{10}{3}+....+\dfrac{10}{9}+\dfrac{10}{10}\)
\(=\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+....+\dfrac{1}{10}\right)\times10\) (1)
Từ (1), suy ra:
\(\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{10}\right)\times x=\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+....+\dfrac{1}{10}\right)\times10\)
\(\Rightarrow x=10\)
Vậy \(x=10\)
~ Học tốt ~
