cho A= 1/1.21 + 1/2.22 + 1/3.23 +...+ 1/80.100; B= 1/1.81 + 1/2.82 + 1/3.83 +...+ 1/20.100 .Tính A/B

Ta có :

`A = 1/(1.21) + 1/(2.22) + 1/(3.23) + ... + 1/(80.100)`

`=> A = 1/20 . (20/(1.21) + 20/(2.22) + 20/(3.23) + ... + 20/(80.100)`

`=> A = 1/20 . (1/1 - 1/21 + 1/2 - 1/22 + 1/3 - 1/23 + ... + 1/80 - 1/100)`

`=> A = 1/20 . [(1/1 + 1/2 + 1/3 + ... + 1/80) - (1/21 + 1/22 + 1/23 + ... +1/100)]`

`=> A = 1/20 . [(1/2 + 1/2 + 1/3 + ... + 1/20) - (1/81 + 1/82 + 1/83+...+ 1/100)]`

`B = 1/(1.81) + 1/(2.82) + 1/(3.83) + ... + 1/(20.100)`

`=> B = 1/80 . (80/(1.81) + 80/(2.82) + 80/(3.83) + ... + 80/(20.100))`

`=> B = 1/80 . (1/1 - 1/81 + 1/2 - 1/82 + 1/3 - 1/83 + ... + 1/20 - 1/100)`

`=> B = 1/80 . [(1/1 + 1/2 + 1/3 + ... + 1/20) - (1/81 + 1/82 + 1/83 + ... + 1/100)]`

`=> A/B = (1/20 . [(1/2 + 1/2 + 1/3 + ... + 1/20) - (1/81 + 1/82 + 1/83+...+ 1/100)])/(1/80 . [(1/1 + 1/2 + 1/3 + ... + 1/20) - (1/81 + 1/82 + 1/83 + ... + 1/100)])`

`=> A/B = (1/20)/(1/80) = 4`

Vậy `A/B = 4`

`#dtkc`