theo đề bài ta có 

                    1+ 1/3 +1/6+...+2/x(x+1)=1+2009/2010

                  =>1/3+1/6+....+2/x(x+1)=2009/2010

                  =>1/2(2+1):2+1/3(3+1):2+.....+1/x(x+1):2=2009/2010

                 =>2/2(2+1)+2(3+1)+....+2/x(x+1)=2009/2010

                 =>2(1/2.3+1/3.4+....+1/x(x+1)=2009/2010

                 =>1/2-1/3+1/3-1/4+.....+1/x-1/x+1=2009/2010:2

                =>1/2-1/x+1=2009/4020

                =>1/x+1=1/2-2009/4020    

                =>1/x+1=1/4020

                =>x+1=4020

                =>x=4020-1

                =>x=4019

`Answer:`

`1/3+1/6+1/10+...+2/(x.(x+1))=2008/2010`

`=2/6+2/12+2/20+...+2/(x.(x+1))=2008/2010`

`=2/(2.3)+2/(3.4)+2/(4.5)+...+(2)/(x.(x+1))=2008/2010`

`=2.(1/2-1/3+1/3-1/4+...+1/x(x+1))=2008/2010`

`=1/2-1/3+1/3-1/4+...+1/x-1/(x+1)=1004/2010`

`=1/2-1/(x+1)=1004/2010`

`=>1/(x+1)=1/2-1004/2010`

`=>1/(x+1)=1/2010`

`=>x+1=2010`

`=>x=2010-1`

`=>x=2009`

1/3+1/6+1/10+2/x.(x+1)=2010/1006

1/6+1/12+1/20+1/x.(x+1)=2010/2012

1/2.3+1/3.4+1/4.5+1/x.(x+1)=1005/1006

1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/x.(x+1)=1005/1006

1/2 - 1/5 + 1/x.(x+1)=1005/1006

3/10+1/x.(x+1)=1005/1006

1/x.(x+1)=1005/1006 - 3/10

1/x.(x+1)=1758/2515

x.(x+1)=1:1758/2515

x.(x+1)=2515/1758

Đến đây thì mình chịu òi!

lm đúng tui tick cho 2 tick!

x= 56 tick tớ nhé 

bạn giải cách làm dc ko?trình bày dễ hỉu mình vào nit phụ tick cho!

Ta có : 1/3+1/6+1/10+ .....+2/x.(x+1)=2010/2012

=>2/6+2/12+2/20+........+2/x(x+1)=2010/2012

=>2.(1/2.3+1/3.4+1/4.5+.....+1/x.(x+1)=2010/2012

                  ................................

Bạn tự làm tiếp nhé ! x=1005

\(1+\frac{1}{3}+\frac{1}{6}+...+\frac{2}{x.\left(x+1\right)}=1\frac{2008}{2010}\)

\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x\left(x+1\right)}=1\frac{2008}{2010}\)

\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=1\frac{2008}{2010}\):2

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2009}{2010}\)

\(\Rightarrow1-\frac{1}{x+1}=\frac{2009}{2010}\)

\(\Rightarrow1-\frac{2009}{2010}=\frac{1}{x+1}\)

\(\Rightarrow\frac{1}{2010}=\frac{1}{x+1}\)

\(\Rightarrow x=2009\)

nha !

Ta có :A=1+\(\frac{2}{6}\)+\(\frac{2}{12}\)+......+\(\frac{2}{x\left(x+1\right)}\)=\(\frac{4018}{2010}\)

\(\Rightarrow\)A=\(\frac{2}{2.3}\)+\(\frac{2}{3.4}\)+...+\(\frac{2}{x\left(x+1\right)}\)=\(\frac{2008}{2010}\)

\(\Rightarrow\)A=2(\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+...+\(\frac{1}{x\left(x+1\right)}\))=\(\frac{2008}{2010}\)

\(\Rightarrow\)A=2(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+...+\(\frac{1}{x}\)-\(\frac{1}{x+1}\))=\(\frac{2008}{2010}\)

\(\Rightarrow\)A=2(\(\frac{1}{2}\)-\(\frac{1}{x+1}\))=\(\frac{2008}{2010}\)

\(\Rightarrow\)A=\(\frac{1}{2}\)-\(\frac{1}{x+1}\)=\(\frac{502}{1005}\)

\(\Rightarrow\)\(\frac{1}{x+1}\)=\(\frac{1}{2010}\)\(\Rightarrow\)x+1=2010\(\Rightarrow\)x=2009