\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x.\left(x+2\right)}=\frac{1005}{2011}\)

\(\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{x.\left(x+2\right)}\right)=\frac{1005}{2011}\)

\(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

\(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

\(\frac{1}{3}-\frac{1}{x+2}=\frac{2010}{2011}\)

\(\frac{1}{x+2}=\frac{1}{3}-\frac{2010}{2011}\)

\(\frac{1}{x+2}=\frac{1}{2011}\)

\(\Rightarrow x+2=2011\)

\(x=2009\)

Đặt biểu thứ là A

2A=2/1.3+2/2.5+...+2/x.x+2

2A=1-1/3+1/3-1/5+.......+1/x-1/x+2

2A=1-1/x+2

x=2009 nha ban

chuc ban hoc gioi

tk cho minh nha

4/5.x-x=1/3

=>x.(4/5-1)=1/3

=>x. ( -1/5)=1/3

=>x=1/3:(-1/5)

=>x= - 5/3

Học tốt !ĐứcTM NgôTM

\(\frac{4}{5x}=\frac{1}{3}\Rightarrow4.3=5x\)

\(\Rightarrow12=5x\)

\(\Rightarrow x=12:5\)

\(\Rightarrow x=\frac{12}{5}\)

Vậy \(x=\frac{12}{5}\)

\(\frac{4}{5}x=\frac{1}{3}\) \(\Rightarrow x=\frac{1}{3}:\frac{4}{5}\)

\(\Rightarrow x=\frac{5}{12}\)

Vậy=...

Bài 1: 1998.1998 - 2000.1996

= 1998.1998 - 1998.1996 - 2.1996

= 2.1998 - 2.1996

= 2.2

= 4

Bài 2:

Bạn viết chưa có vế phải nên không tính được.

Bài 1: = 2000 - 1996 = 4

BÀi 2: Dễ! tự làm nha

 Kết quả bằng 4 đấy anh em !!!   

giùm em nha mấy anh 

\(2M=2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{98}}\)

Lấy 2M-M theo từng vế ta được:

\(2M-M=2+1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}-...-\frac{1}{2^{98}}\)\(-1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{99}}\)

\(M=2-\frac{1}{2^{99}}\)

Ko tính ra được kết quả cụ thể

\(S=\frac{2010^2}{2010x}+\frac{1}{2010y}-\frac{2010}{1005}\ge\frac{2011^2}{2010\left(x+y\right)}-\frac{2010}{1005}\)

\(\frac{2011^2}{2010.\frac{2011}{2012}}-\frac{2010}{1005}=\frac{2021056}{1005}\)

a)3.061

b)0.0022

Đáp án:A 8,573:2,8 = 3,061

            B Số Dư Của Phép Chia Trên Là: 0,22

\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+....+\frac{1}{x\times\left(x+2\right)}=\frac{1005}{2011}\)

\(\Leftrightarrow\frac{1}{2}\times\left(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+.....+\frac{1}{x\times\left(x+2\right)}\right)=\frac{1005}{2011}\)

\(\Leftrightarrow\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

\(\Leftrightarrow\frac{1}{2}\times\left(1-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

\(\Leftrightarrow1-\frac{1}{x+2}=\frac{1005}{2011}:\frac{1}{2}=\frac{2010}{2011}\)

\(\Leftrightarrow\frac{1}{x+2}=1-\frac{2010}{2011}=\frac{1}{2011}\)

\(\Leftrightarrow x+2=2011\)

\(\Leftrightarrow x=2009\)

Vậy x = 2009

\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{x\left(x+2\right)}=\frac{1005}{2011}\)

\(\Rightarrow\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{x\left(x+2\right)}=\frac{1005}{2011}\)

\(\Rightarrow\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

\(\Rightarrow\frac{1}{2}\left(1-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

\(\Rightarrow\frac{x+1}{x+2}=\frac{2010}{2011}\)

\(\Rightarrow x+1=2010\Leftrightarrow x=2009\)

\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+.......+\frac{1}{x.\left(x+2\right)}=\frac{1005}{2011}\) 

<=> \(\frac{1}{1.3}+\frac{1}{3.5}+......+\frac{1}{x.\left(x+2\right)}=\frac{1005}{2011}\)

<=>\(\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+......+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

<=>\(\frac{1}{2}.\left(1-\frac{1}{x+2}\right)=\frac{1005}{2011}\)

<=> \(1-\frac{1}{x+2}=\frac{1005}{2011}:\frac{1}{2}\)

<=> \(1-\frac{1}{x+2}=\frac{2010}{2011}\) <=> \(\frac{1}{x+2}=1-\frac{2010}{2011}\)

                                                     <=> \(\frac{1}{x+2}=\frac{1}{2011}\) <=>  \(x+2=2011\)<=> \(x=2009\)

vậy \(x=2009\)

Gọi \(A=\frac{1005}{2011}\)

A=1/3 + 1/3.5 + 1/5.7 +...............+1/x.(x+2)

A=1/1.3 + 1/3.5 + 1/5.7 +...............+1/x.(x+2)

A . 2=2/1.3 + 2/3.5 + 2/5.7 +......................+2/x.(x+2)

A . 2=1/1-1/3+1/3-1/5+1/5-1/7+..............+1/x-1/x+2

A . 2=1/1+(1/3-1/3)+(1/5-1/5)+..............+(1/x-1/x)-1/x+2

A . 2=1/1-1/x+2

Suy gia:1005/2011 . 2=1/1-1/x+2

             2010/2011    =1/1-1/x+2

             1/x+2           =1/1-2010/2011

              1/x+2          =1/2011

Suy gia:x+2=2011

            x    =2011-2

            x    =2009