=>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

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

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

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

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

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

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

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

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Trần Thị Loan chuẩn rồi 

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

\(2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2013}{2015}:2\)

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

tự làm tiếp nhé mk ăn cơm đã

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

\(A=\frac{1}{3}+\frac{1}{6}+...+\frac{2}{x\left(x+1\right)}=\frac{2013}{2015}\)

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

\(\Rightarrow A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}\right)=\frac{2013}{2015}\)

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

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

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2013}{4050}\)

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

=> x + 1 = 2015 

=> x = 2014 

ai nhanh minh k cho

2014 bạn ơi

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{2013.2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\left(\frac{1}{1}-\frac{1}{2015}\right)=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{2}\cdot\frac{2014}{2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1007}{2015}=\frac{1}{2}-\frac{1}{x}\)

\(\Leftrightarrow\frac{1}{x}=\frac{1}{2}-\frac{1007}{2015}\Leftrightarrow\frac{1}{x}=\frac{1}{4030}\)

\(\Rightarrow x=4030\)

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