Đáp án:
Bài `9.`
`A=-2`
Bài `10,`
`a, A=(-197)/199`
`b, B=133/195`
Giải thích các bước giải:
Bài `9.`
`A =(5/3 - 3/7 + 9) - (2+5/7 - 2/3) + (8/7 - 4/3 - 10)`
`⇔ A = 5/3 - 3/7 + 9 -2-5/7 + 2/3 + 8/7 - 4/3 - 10`
`⇔ A = (5/3 + 2/3- 4/3) + (-3/7 - 5/7 + 8/7) + (9-2 - 10)`
`⇔A=1 + 0 -3`
`⇔A=1-3`
`⇔A=-2`
Vậy `A=-2`
Bài `10.`
`a,`
`A=1/199 - 1/(199 × 198) - 1/(198×197) - ... - 1/(3×2) - 1/(2×1)`
`⇔ A = 1/199 - [1/(1×2) + 1/(2×3) + ... + 1/(197×198) + 1/(198 × 199)]`
`⇔ A = 1/199 -[1-1/2 + 1/2 - 1/3 + ... + 1/197 - 1/198 + 1/198 - 1/199]`
`⇔ A = 1/199 - [1 + (-1/2 + 1/2) + ... + (-1/198 + 1/198) - 1/199]`
`⇔ A = 1/199 - [1 - 1/199]`
`⇔ A = 1/199 - 1 + 1/199`
`⇔ A = (1/199 + 1/199) - 199/199`
`⇔ A = 2/199 - 199/199`
`⇔ A = (-197)/199`
Vậy `A=(-197)/199`
`b,`
`B=1 -2/(3×5) - 2/(5×7) - ... - 2/(61×63) - 2/(63×65)`
`⇔B = 1 - [2/(3×5) + 2/(5×7) + ... + 2/(61×63) + 2/(63×65)]`
`⇔B=1 - [1/3-1/5 + 1/5 - 1/7 + ... + 1/61 - 1/63 + 1/63 - 1/65]`
`⇔B=1-[1/3 + (-1/5 + 1/5) + ... + (-1/63 + 1/63) - 1/65]`
`⇔ B = 1-[1/3 - 1/65]`
`⇔B=1-[65/195 - 3/195]`
`⇔B=1-62/195`
`⇔B=195/195-62/195`
`⇔B=133/195`
Vậy `B=133/195`
