`# \text {04th5}`
`1)`
`A=1/(11*12) + 1/(12*13) + ... + 1/(54*55)`
`= 1/11 - 1/12 + 1/12 - 1/13 + ... + 1/54 - 1/55`
`= 1/11 - (1/12 - 1/12) - (1/13 - 1/13) - ... - 1/55`
`= 1/11 - 1/55`
`=4/55`
Vậy, `A = 4/55`
`2)`
`A = 2/(1*3) + 2/(3*5) + ... + 2/(9*11)`
`= 1 - 1/3 + 1/3 - 1/5 + ... + 1/9 - 1/11`
`= 1 - (1/3 - 1/3) - ... - 1/11`
`= 1 - 1/11`
`= 10/11`
Vậy, `A = 10/11`
3); 4); 5) Tương tự!
`6)`
`A = 1/(1*3) + 1/(3*5) + ... + 1/(19*21)`
`= 1/2*(2/(1*3) + 2/(3*5) + ... + 2/(19*21))`
`= 1/2*(1 - 1/3 + 1/3 - 1/5 + ... + 1/19 - 1/21)`
`= 1/2*[ 1 - (1/3 - 1/3) - ... - 1/21]`
`= 1/2*(1 - 1/21)`
`= 1/2*20/21`
`=10/21`
Vậy, `A = 10/21`
`7)`
`1/(4*9) + 1/(9*14) + ... + 1/(54*59)`
`= 1/5*(5/(4*9) + 5/(9*14) + ... + 5/(54*59))`
`= 1/5* (1/4 - 1/9 + 1/9 - 1/14 + ... + 1/54 - 1/59)`
`= 1/5* [ 1/4 - (1/9 - 1/9) - ... - 1/59]`
`= 1/5*(1/4 - 1/59)`
`= 1/5 * 55/236`
`= 11/236`
Vậy, `A = 11/236`
`8)`
`A = 1/(1*5) + 1/(5*9) + ... + 1/(97*101)`
`= 1/4*(4/(1*5) + 4/(5*9) + ... + 4/(97*101))`
`= 1/4*(1 - 1/5 + 1/5 - 1/9 + ... + 1/97 - 1/101)`
`= 1/4 * [1 - (1/5 - 1/5) - ... - 1/101]`
`= 1/4*(1 - 1/101)`
`= 1/4*100/101`
`= 25/101`
Vậy, `A = 25/101.`