Đáp án:
`x=21`
Giải thích các bước giải:
`(x-20).(1/2+1/3+1/4+...+1/200)/(1/199+2/198+3/197+...+198/2+199/1)=1/200`
`=>(x-20).(1/2+1/3+1/4+...+1/200)/(1/199+2/198+3/197+...+198/2+199/1+(199-199))=1/200`
`=>(x-20).(1/2+1/3+1/4+...+1/200)/(1/199+2/198+3/197+...+198/2+199/1+( \underbrace{1+1+1+...+1}_{\text{ Có 199 số 1}}-199))=1/200`
`=>(x-20).(1/2+1/3+1/4+...+1/200)/((1/199+1)+(2/198+1)+(3/197+1)+...+(198/2+1)+(199/1+1)-199)=1/200`
`=>(x-20).(1/2+1/3+1/4+...+1/200)/((1/199+199/199)+(2/198+198/198)+(3/197+197/197)+...+(198/2+2/2)+(199/1+1/1)-199)=1/200`
`=>(x-20).(1/2+1/3+1/4+...+1/200)/(200/199+200/198+200/197+...+200/2+200 -199)=1/200`
`=>(x-20).(1/2+1/3+1/4+...+1/200)/(200/199+200/198+200/197+...+200/2+200/200 )=1/200`
`=>(x-20).(1/2+1/3+1/4+...+1/200)/(200.(1/199+1/198+1/197+...+1/2+1/200))=1/200`
`=>(x-20). 1/200=1/200`
`=>x-20=1/200:1/200`
`=>x-20=1`
`=>x=1+20`
`=>x=21`
Vậy `x=21`
