Đáp án:
`A/B=1`
Giải thích các bước giải:
`A/B = (1/51 + 1/52+... + 1/100)/(1/(1.2) + 1/(3.4)+...+1/(99.100)`
Xét : `B = 1/(1.2)+1/(3.4) +...+1/(99.100)`
`->B = (2-1)/(1.2) + (4-3)/(3.4)+...+(100-99)/(99.100)`
`->B = 1 - 1/2 + 1/3 - 1/4 + ... + 1/99 - 1/100`
`->B = (1 + 1/3 + ... + 1/99) - (1/2 + 1/4 + ... + 1/100)`
`->B = (1+1/3 +...+1/99) - (1/2+1/4+...+1/100) - (1/2+1/4+...+1/100) + (1/2+1/4 + ... + 1/100)`
`->B = (1+1/3+...+1/99) - 2 (1/2 +1/4+...+1/100) + (1/2 +1/4+...+1/100)`
`->B = (1+1/2 + 1/3+...+1/99 + 1/100) - (1 + 1/2+...+1/50)`
`->B = 1+1/2+...+1/100 - 1-1/2-...-1/50`
`->B=(1-1)+(1/2-1/2)+...+(1/50-1/50) + 1/51 + 1/52 +...+1/100`
`->B=1/51+1/52+...+1/100`
`->A/B=(1/51+1/52+...+1/100)/(1/51+1/52+...+1/100)`
`->A/B=1`
Vậy `A/B=1`
