`1/3` `+` `1/6` `+` `1/10` `+` `...` `+` `2/(x(x+1))` ``=` `2013/2015`
2 câu trả lời
`1/3+1/6+...+2/(x(x+1))=2013/2015(x\ne 0,x\ne -1)`
`->2/6 +2/12+...+2/(x(x+1))=2013/2015`
`-> 2/(2.3) +2/(3.4)+...+2/(x(x+1))=2013/2015`
`-> 2 (1/2-1/3+1/3-1/4+...+1/x-1/(x+1))=2013/2015`
`->1/2 - 1/(x+1)=2013/4030`
`->1/(x+1)=1/2015`
`->x+1=2015`
`->x=2014` (Tm)
Vậy `x=2014`
`1/3+1/6+1/10+...+2/(x(x+1))=2013/2015(x\ne0; x\ne-1)`
`<=>2/6+2/12+2/20+...+2/(x(x+1))=2013/2015`
`<=>2[1/6+1/12+1/20+...+1/(x(x+1))]=2013/2015`
`<=>2[1/2.3+1/3.4+1/4.5+...+1/(x(x+1))]=2013/2015`
`<=>2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/(x+1))=2013/2015`
`<=>2(1/2-1/(x+1))=2013/2015`
`<=>1-2/(x+1)=2013/2015`
`<=>2/(x+1)=2/2015`
`=>x+1=2015`
`<=>x=2014(TM)`
Vậy `x=2014`
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