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`

Câu 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 = 97`

`#dtkc`

Đáp án + Giải thích các bước giải:

Câu `1`:

`a)`

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

`->` `(5/7 : 3/4) . 2/5 + 13/21`

`->` `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`

`->` `frac{16 . 25 . 36 . ... . 10000}{15 . 24 . 35 . ... . 9999}`

`->` `frac{4 . 4 . 5 . 5 . 6 . 6 . ... . 100 . 100}{3 . 5 . 4 . 6 . 5 . 7 . ... . 99 . 101}`

`->` `frac{4 . 100}{3 . 4 . 101}`

`->` `frac{100}{3 . 101}`

`->` `frac{100}{303}`

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

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

`->` `frac{2}{3 . 5}` + `frac{2}{5 . 7}` + `frac{2}{7 . 9}` + ... + `frac{2}{y . (y + 2)}` = `16/99 . 2`

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

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

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

`->` `frac{1}{y + 2}` = `frac{1}{99}`

`->` `y + 2 = 99`

`->` `y = 97`