2 câu trả lời
Sửa:
`1/21 + 1/28 + 1/36 + ... + 2/(x.(x + 1)) = 2/9`
`2/42 + 2/56 + 2/72 + ... + 2/(x.(x + 1)) = 2/9`
`2/(6.7) + 2/(7.8) + 2/(8.9) + ... + 2/(x.(x + 1) = 2/9`
`1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + ... + 1/x - 1/(x + 1) = 2/9`
`1/6 - 1/(x + 1) = 2/9`
`1/(x + 1) = 1/6 - 2/9`
`1/(x + 1) = -1/18`
`1 . 18 = -1 . (x + 1)`
`18 = -x - 1`
`-x = 18 + 1`
`-x = 19`
`x = -19`
Vậy `x = -19`
`1/21 + 1/28 + 1/36 + ... + 2/{ x. ( x - 1 )} = 2/9`
`=> 2/42 + 2/56 + 2/72 + ... + 2/{ x. ( x - 1 )} = 2/9`
`=> 2/{ 6.7 } + 2/{7.8} + 2/{8.9} + ... 2/{ ( x - 1 )x } = 2/9`
`=> 2( 1/{ 6.7 } + 1/{7.8} + 1/{8.9} + ... 1/{ ( x - 1 )x } ) = 2/9`
`=> 2( 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + ... + 1/{x-1} - 1/x ) = 2/9`
`=> 2( 1/6 - 1/x ) = 2/9`
`=> 1/3 - 2/x = 2/9`
`=> 2/x = 1/3 - 2/9`
`=> 2/x = 1/9`
`=> x = 2 : 1/9`
`=> x = 18`
$Vậy$ `x =18`