Câu 1

`a ) ( 5/7 : 3/4 ) × 2/5 + 131313/212121`

`= 20/21 × 2/5 + 13/21`

`= 8/21 + 13/21`

`= 1`

`b ) ( 1 + 1/15 ) × ( 1 + 1/24 ) × ( 1 + 1/35 ) × ... × ( 1 + 1/9999 )`

`= 16/15 × 25/24 × 36/35 × ... × 10000/9999`

`= {16 × 25 × 36 × ... × 10000}/{15 × 24 × 35 × ... × 9999}`

`= {4 × 4 × 5 × 5 × 6 × 6 × ... × 100 × 100}/{3 × 5 × 4 × 6 × 5 × 7 × ... × 99 × 101}`

`= {4 × 100}/{3 × 4 × 101}`

`= 100/303`

Bài 2

`a ) y × 3 - y × 7/5 = 11,2`

`y × ( 3 - 7/5 ) = 11,2`

`y × 1,6 = 11,2`

          `y = 11,2 : 1,6`

          `y = 7`

`b ) 1/{3 × 5} + 1/{5 × 7} + 1/{7 × 9} + ... + 1/{y × ( y + 2 )} = 16/99`

`2 × ( 1/{3 × 5} + 1/{5 × 7} + 1/{7 × 9} + ... + 1/{y × ( y + 2 )} = 16/99 × 2`

` 2/{3 × 5} + 2/{5 × 7} + 2/{7 × 9} + ... + 2/{y × ( y + 2 )} = 32/99`

`1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/y - 1/{y + 2} = 32/99`

`1/3 - 1/{y + 2} = 32/99`

`1/{y + 2} = 1/3 - 32/99`

`1/{y + 2} = 1/99`

`=> y + 2 = 99`

            `y = 99 - 2`

            `y = 97`

`#dtkc`

`1,`

`a) ( 5/7 : 3/4 ) xx 2/5 + 131313/21212`

`=20/21 xx 2/5 + 13/211`

`= 8/21 + 13/21`

`= 1`

`b) ( 1 + 1/15 ) xx ( 1 + 1/24 ) xx ( 1 + 1/35 ) xx .... xx ( 1 + 1/9999 )`

`= 16/15 xx 25/24 xx 36/35 xx .... xx 10000/9999`

`= ( 16 xx 25 xx 36 xx .... xx 10000 )/( 15 xx 24 xx 35 xx .... xx 9999 )`

`= ( 4 xx 4 xx 5 xx 5 xx 6 xx 6 xx .... xx  100 xx 100 )/( 3 xx 5 xx 4 xx 6 xx 5 xx 7 xx .... xx 99 xx 101 )`

`= ( ( 4 xx 5 xx 6 xx .... xx 100 ) xx ( 4 xx 5 xx 6 xx .... xx 100 ) )/( ( 3 xx 4 xx 5 xx .... xx 99 ) xx ( 5 xx 6 xx 7 xx .... xx 101 ) )`

`= ( 100 xx 4 )/( 3 xx 4 xx 101 )`

`= 100/303`

`2,`

`a) y xx 3 - y xx 7/5 = 11,2`

       `y xx ( 3 - 7/5 ) = 11,2`

              `y xx 8/5   = 11,2`

                    `y        = 11,2 : 8/5`

                    `y        = 7`

Vậy `, y = 7 .`

`b) 1/( 3 xx 5 ) + 1/( 5 xx 7 ) + 1/( 7 xx 9 ) + .... + 1/( y xx ( y + 2 ) ) = 16/99`

`2 xx ( 1/( 3 xx 5 ) + 1/( 5 xx 7 ) + 1/( 7 xx 9 ) + .... + 1/( y xx ( y + 2 ) ) ) = 16/99 xx 2`

`2/( 3 xx 5 ) + 2/( 5 xx 7 ) + 2/( 7 xx 9 ) + .... + 2/( y xx ( y + 2 ) ) = 32/99`

`1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + .... + 1/y - 1/( y + 2 ) = 32/99`

`1/3 - 1/( y + 2 ) = 32/99`

`1/( y + 2 ) = 1/3 - 32/99`

`1/( y + 2 ) = 1/99`

`y + 2 = 99`

`y = 99 - 2`

`y = 97`

Vậy `, y = 97 .`