Tìm x, biết : 1/3 + 1/6 +1/10 + ... + 2/x(x+1)=2015/2017

Đáp án `+` Giải thích các bước giải :

`1/3 + 1/6 +1/10 + ... + 2/x(x+1)=2015/2017`

`2/6+2/12+2/20+...+(2)/(x(x+1))=2015/2017`

`2/(2xx3)+2/(3xx4)+2/(4xx5)+...+2/(x(x+1))=2015/2017`

`2xx(1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/(x+1)=2015/2017`

`2xx(1/2-1/(x+1)=2015/2017`

`1/2-1/(x+1)=(2015)/(2017) : 2/5`

`1/2-1/(x+1)=2015/4034`

`1/(x+1)=1/2-(2015)/(4034)`

`1/(x+1)=(2017)/(4034)-(2015)/(4034)`

`1/(x+1)=2/2034`

`1/(x+1)=1/2017`

`=> x + 1 = 2017`

`=> x       = 2017-1`

`=> x       = 2016`