Tìm số tự nhiên x 2/5.8 + 2/8.11 +2/11.14 + ..........+ 2/ x.(x+3) = 101/770 cíu

Đáp án + Giải thích các bước giải:

`2/5.8+2/8.11+2/11.14+...+2/(x(x+3))=101/770`

`=>2/3[3/5.8+3/8.11+3/11.14+...+3/(x(x+3))]=101/770`

`=>1/5-1/8+1/8-1/11+1/11-1/14+...+1/x-1/(x+3)=101/770:2/3`

`=>1/5-1/(x+3)=101/770. 3/2`

`=>1/5-1/(x+3)=303/1540`

`=>1/(x+3)=1/5-303/1540`

`=>1/(x+3)=308/1540-303/1540`

`=>1/(x+3)=1/308`

`=>x+3=308`

`=>x=308-3`

`=>x=305`

Vậy `x=305`

Đáp án+Giải thích các bước giải:

`2/{5.8} + 2/{8.11} + 2/{11.14} + ... + 2/{x.(x+3)}) = 101/770`

`⇒ 2/3(3/{5.8} + 3/{8.11} + 3/{11.14} + ... + 3/{x.(x+3)}) = 101/770`

`⇒ 2/3(1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + ... + 1/x - 1/{x+3}) = 101/770`

`⇒ 2/3(1/5 - 1/{x+3}) = 101/770`

`⇒ 1/5 - 1/{x+3} = 101/770 : 2/3`

`⇒ 1/5 - 1/{x+3} = 303/1540`

`⇒ 1/{x+3} = 1/5 - 303/1540`

`⇒ 1/{x+3} = 1/308`

`⇒ x + 3 = 308`

`⇒ x = 308 - 3`

`⇒ x = 305`

Vậy `x = 305`