Đáp án:
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`a,`
`1/2 - 1/(3×7) - 1/(7×11) - ... - 1/(19 × 23) - 1/(23 × 27)`
`= 1/2 - [1/(3×7) + 1/(7×11) + ... + 1/(19×23) + 1/(23×27) ]`
`= 1/2 - 1/4 × [1/3 - 1/7 + 1/7 - 1/11 + ... + 1/19 - 1/23 + 1/23 - 1/27]`
`= 1/2 - 1/4 × [1/3 + (-1/7 + 1/7) + ... + (-1/23 + 1/23) - 1/27]`
`= 1/2 - 1/4 × [1/3 - 1/27]`
`= 1/2 - 1/4 × [9/27 - 1/27]`
`= 1/2 - 1/4 × 8/27`
`= 1/2 - 2/27`
`= 23/54`
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`b,`
`1 - 1/(5×10) - 1/(10 × 15) - ... - 1/(90 × 95) - 1/(95 × 100)`
`= 1 - [1/(5×10) + 1/(10×15) + ... + 1/(90×95) + 1/(95 × 100) ]`
`= 1 - 1/5 × [1/5 - 1/10 + 1/10 - 1/15 + ... + 1/90 - 1/95 + 1/95 - 1/100]`
`= 1 - 1/5 × [1/5 + (-1/10 + 1/10) + ... + (-1/95 + 1/95) - 1/100]`
`= 1 - 1/5 × [1/5 - 1/100]`
`= 1 - 1/5 × [20/100 - 1/100]`
`= 1 - 1/5 × 19/100`
`= 1 - 19/500`
`= 481/500`