Tính hợp lý: 1/2 + 5/6 +11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90 Làm và cho các dạng bài tương tự

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1. `1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90`

   `= ( 1 – 1/2 ) + ( 1 – 1/6 ) + ( 1 – 1/12 ) + ( 1 -1/20 ) + ( 1 – 1/30 ) + ( 1 – 1/42 ) + ( 1 – 1/56 ) + ( 1 – 1/72 ) + ( 1 – 1 /90 )`

   `= ( 1 + 1 + … + 1 ) – ( 1/2 + 1/6 + 1/12 + … + 1/90 )`

   `= 1 . 9 – ( 1/( 1 . 2 ) + 1/( 2 . 3 ) + 1/( 3 . 4 ) + … + 1/( 9 . 10 )`

   `= 9 – ( 1/1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + … + 1/9 – 1/10 )`

   `= 9 – ( 1 – 1/10 )`

   `= 9 – 9/10`

   `= 81/10`

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2. `1/2 + 5/6 +11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72 + 89/90`

   `= 1 – 1/2 + 1 – 1/6 + 1 – 1/20 + 1 – 1/30 + 1 – 1/42 + 1 – 1/56 + 1 – 1/72 + 1 – 1/90`

   `= 9 – (1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72+ 1/90)`

   `= 9 – (1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9+ 1/9.10)`

   `= 9 – (1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + 1/6 – 1/7 + 1/7 – 1/8 + 1/8 – 1/9 + 1/9 – 1/10)`

   `= 9 – (1 – 1/10)`

   `= 9 – ( 10/10 – 1/10 )`

   `= 9 – 9/10 = 90/10 – 9/10`

   `= 81/10`

    

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