Rút gọn: a) A= $\frac{3}{1.4}$ + $\frac{3}{4.7}$ + $\frac{3}{7.10}$ +...+ $\frac{3}{100.103}$ b) B= $\frac{2}{1.5}$ + $\frac{2}{5.9}$ + $\frac{2}{9.13}$ +...+ $\frac{2}{2021.2021}$ Ví dụ câu a bước đầu là: =3.($\frac{1}{1.4}$ + $\frac{1}{4.7}$ + $\frac{1}{7.10}$ +...+ $\frac{1}{100.103}$ Bước tiếp theo làm thế nào?Câu B làm tương tự giúp mk!!! Nhanh=hay nhất!!!

`a) A = 3/( 1. 4 ) + 3/( 4.7 ) + 3/( 7. 10 ) + ... + 3/( 100. 103 ) `

   `= (4 - 1)/( 1. 4 ) + (7 - 4)/( 4. 7 ) + ( 10 - 7 )/( 7. 10 ) + ... + ( 103 - 100 )/( 100. 103 )`

   `= 4/( 1. 4 ) - 1/( 1. 4 ) + 7/( 4. 7 ) - 4/( 4. 7 ) + 10/( 7. 10 ) - 7/( 7. 10 ) + ... + 103/( 100. 103 ) - 100/( 100. 103 )`

   `= 1/1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/100 - 1/103`

   `= 1 - 1/103`

   `= 102/103`

 `b) B = 2/( 1. 5 ) + 2/( 5. 9 ) + 2/( 9. 13 ) + ..... + 2/( 2021. 2025 )`

   `B. 2 = 4/( 1. 5 ) + 4/( 5. 9 ) + 4/( 9. 13 ) + .... + 4/( 2021. 2025 )`

         `= ( 5 - 1 )/( 1. 5 ) + ( 9 - 5 )/( 5. 9 ) + ( 13 - 9 )/( 9. 13 ) + .... + ( 2025 - 2021 )/( 2021. 2025 )`

  `= 5/(1.5) - 1/(1.5) + 9/(5. 9) - 5/(5. 9) + 13/(9. 13) - 9/(9. 13) + ... + 2025/(2021. 2025) - 2021/(2021. 2025)`

  `= 1/1 - 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + .... + 1/2021 - 1/2025`

 `= 1 - 1/2025`

`B. 2 = 2024/2025`

  `B = 2024/2025 : 2`

  `B = 1012/2025`

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