=>2/6+2/12+2/20+...+2/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

=>(1/2-1/x+1)=2013/2015:2

=>-(1/x+1)=2013/4030-1/2

=>-(1/x+1)=-(1/2015)=>x+1=2015=>x=2014

\(\Rightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+....+\frac{2}{x\cdot\left(x+1\right)}=\frac{2013}{2015}\)

\(\Rightarrow2.\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{x\cdot\left(x+1\right)}\right)=\frac{2013}{2015}\)

\(\Rightarrow2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{x\cdot\left(x+1\right)}\right)=\frac{2013}{2015}\)

\(\Rightarrow2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2013}{2015}\)

\(\Rightarrow\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2013}{2015}:2\)

\(\Rightarrow-\frac{1}{x+1}=\frac{2013}{4030}-\frac{1}{2}\)

\(\Rightarrow-\frac{1}{x+1}=-\frac{1}{2015}\Rightarrow x+1=2015\Rightarrow x=2014\)

bạn trên trả lời đúng rùi đó

Trần Thị Loan chuẩn rồi 

2/6+2/12+2/20+...+2/x(x+2)=2013/2015

2(1/2.3+1/3.4+...+1/x(x+1))=2013/2015

2(1/2-1/3+1/3-1/4+...+1/x-1/x+1)=2013/2015

2(1/2-1/x+1)=2013/2015

1/2-1/x+1=2013/2015:2

1/2-1/x+1=2013/4030

1/x+1=1/2-2013/4030

1/x+1=1/2015

Suy ra x+1=2015

x=2014

Vậy x=2014

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

1/2.3+1/3.4+1/4.5+...+1/x.(x+1)=2013/4030

1/2-1/3+1/3-1/4+...+1/x-1/x+1=2013/4030

1/2-1/x+1=2013/4030

1/x+1=1/2015

=> x+1=2015

     x=2014

Vậy x=2014

Đặt A=Vế trái

Ta có :

\(A \over 2 \)\(= \)\({1\over 6 } +{1\over 12 }+{1\over 20 }+...+{1\over x(x+1)}\)

   =\({1\over 2}-{1\over 3}+{1\over 3}-{1\over 4}+{1\over4}-{1\over 5}+...+{1\over x-1}-{1\over x}+{1\over x}-{1\over x+1}\)

   =\({1\over2}-{1\over x+1}\)

Từ đó suy ra: \({1\over2}-{1\over x+1}={2013\over4030}\)

=> x=2014

tk mk , mk tk 

a) \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)

\(\Rightarrow\frac{x+1}{10}+\frac{x+1}{11}+\frac{x+1}{12}-\frac{x+1}{13}-\frac{x+1}{14}=0\)

\(\Rightarrow\left(x+1\right)\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\right)=0\)

Vì \(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}-\frac{1}{13}-\frac{1}{14}\ne0\) nên x+1=0

=>x=0-1

=>x-1

a:x+1/10+x+1/11+x+1/12=x+1/13+x+1/14

 <=>(x+1)(1/10 + 1/11+1/12) =(x+1)(1/13 + 1/14) 
<=>(x+1)(1/10 + 1/11+1/12 -1/13 -1/14)=0 
<=> x+1=0(vì biểu thức 1/10 + 1/11 +1/12-1/13-1/14#0) 
<=>x= -1

b:hình như sai đề