`(9/(2 . 3)+ 9/(3 . 4) + ... + 9/(199 . 200)) . x= 2/5`
`=> 9 . (1/2 - 1/3 + 1/3 - 1/4 + 1/4 - ... - 1/199 + 1/199 - 1/200) . x = 2/5`
`=> 9 . (1/2 - 1/200) . x = 2/5`
`=> 9 . 99/200 . x = 2/5`
`=> 891/200 . x = 2/5`
`=> x = 2/5 : 891/200`
`=> x=80/891`
Vậy: `x=80/891`
`(9/2*3 + 9/3*4 + ... + 9/199*200) * x = 2/5`
`=> 9*(1/2*3 + 1/3*4 + ... +1/199*200) * x = 2/5`
`=> 9*(1/2 - 1/3 + ... + 1/199 - 1/200) * x = 2/5`
`=> 9*(1/2 - 1/200) * x = 2/5`
`=> 9* 99/200 * x = 2/5`
`=> 891/200 * x = 2/5`
`=> x = 2/5 : 891/200`
`=> x = 80/891`
\(\left(\dfrac{9}{2.3}+\dfrac{9}{3.4}+...+\dfrac{9}{199+200}\right).x=\dfrac{2}{5}\)
\(9.\left(\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{199+200}\right).x=\dfrac{2}{5}\)
\(9.\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{199}+\dfrac{1}{200}\right).x=\dfrac{2}{5}\)
\(9.\left(\dfrac{1}{2}-\dfrac{1}{200}\right).x=\dfrac{2}{5}\)
\(9.\left(\dfrac{100}{200}-\dfrac{1}{200}\right).x=\dfrac{2}{5}\)
\(9.\dfrac{99}{200}.x=\dfrac{2}{5}\)
\(\dfrac{891}{200}.x=\dfrac{2}{5}\)
\(x=\dfrac{2}{5}:\dfrac{891}{200}\)
\(x=\dfrac{2}{5}.\dfrac{200}{891}\)
\(x=\dfrac{400}{4455}=\dfrac{80}{891}\)