Đáp án:
`x=10`
Giải thích các bước giải:
`(1/1.101+1/2.102+1/3*103+..+1/10*110)x=1/(1*11)+1/(2*12)+1/(3*13)+...+1/(100*101)`
`1/100.(100/1.101+100/2.102+100/3.103+..+100/10.110)x=1/10(10/(1*11)+10/(2*12)+10/(3*13)+...+10/(100*101))`
`1/100.(1-1/100+1/2-1/102+1/3-1/103+...+1/10-1/110)x=1/10(1-1/11+ 1/2-1/12+1/3-1/13+...+1/100-1/101)`
`1/100.[(1+1/2+1/3+...+1/10)-(1/100+1/102+1/103+...+1/110)]x=1/10[(1+1/2+1/3+...+1/100)-(1/11+1/12+1/13+...+1/101)]`
`1/100.[(1+1/2+1/3+...+1/10+1/11+1/12+1/13+...+1/100)-(1/11+1/12+1/13+...+1/100+1/102+1/103+...+1/110)]x=1/10[(1+1/2+1/3+...+1/100)-(1/11+1/12+1/13+...+1/101+1/102+...+1/110)]`
`1/100.x:1/10=[(1+1/2+1/3+...+1/100)-(1/11+1/12+1/13+...+1/101+1/102+...+1/110)]:[(1+1/2+1/3+...+1/10+1/11+1/12+1/13+...+1/100)-(1/11+1/12+1/13+...+1/100+1/102+1/103+...+1/110)]`
`1/100.x:1/10=1`
`1/100.x=1*1/10`
`1/100.x=1/10`
`x=1/10:1/100`
`x=1/10*100/1`
`x=10`
