Question

(1/2+1/3+1/4+...+1/10)×x=1/9+2/8+3/7+...+9/1

 

Answer 1

\(\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{10}\right)\) . x = \(\dfrac{1}{9}+\dfrac{2}{8}+\dfrac{3}{7}+...+\dfrac{9}{1}\)

Biến đổi vế phải 

\(\dfrac{1}{9}+\dfrac{2}{8}+\dfrac{3}{7}+...+\dfrac{9}{1}\) 

= \(\left(\dfrac{1}{9}+1\right)+\left(\dfrac{2}{8}+1\right)+\left(\dfrac{3}{7}+1\right)+...+\left(\dfrac{8}{2}+1\right)+1\)   

= \(\dfrac{10}{10}+\dfrac{10}{9}+\dfrac{10}{8}+\dfrac{10}{7}+...+\dfrac{10}{2}\)

= \(10\left(\dfrac{1}{10}+\dfrac{1}{9}+\dfrac{1}{8}+...+\dfrac{1}{2}\right)\)

⇒ x = 10