Gọi F= 4/2.4+4/4.6+4/6.8+...+4/2008.2010
F/2= 2/2.4+2/4.6+...+2/2008.2010
Mà 2/2.4=1/2-1/4; 2/4.6=1/4-1/6 ....
Vậy F/2= (1/2-1/4)+(1/4-1/6)+....+(1/2008-1/2010)
F/2=1/2-1/2010=2010/4020-2/4020=2008/4...
F= 2008.2/4020=1004/1005

F=2 .(1/2-1/4+1/4-1/6+......+1/2008 - 1/2010)

  = 2.(1/2-1/2010)

  = 2. 502/1005

  = 1004/1005

Ta có: \(F=\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{2008\cdot2010}\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)

\(=2\cdot\left(\dfrac{1}{2}-\dfrac{1}{2010}\right)\)

\(=2\cdot\dfrac{502}{1005}=\dfrac{1004}{1005}\)

\(F=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2008.2010}\)

\(F=2.\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{2008.2010}\right)\)

\(F=2.\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)

\(F=2.\left(\dfrac{1}{2}-\dfrac{1}{2010}\right)\)

\(F=1-\dfrac{1}{1005}=\dfrac{1004}{1005}\)

=2(2/2.4+2/4.6+......+22/008.2010)

=2(12−12010)

F=2\ 2/2.4+2/4.6+2/6.8+.....+2/2008.2010  \

  =2  \ 1/2-1/4+1/4-1/6+1/6-1/8+.....+1/2008-1/2010  \

  =2   \ 1/2-1/2010 \ =2  \  502/1005  \  =1004/1005

chú ý : \ là ngoặc 

\(F=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(F=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(F=2.\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(F=2.\frac{502}{1005}\)

\(F=\frac{1004}{1005}\)

nhinf vào là biết luật ngay bài đó bằng = \(\frac{1004}{1005}\)

kết bạn với mình nha

\(F=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

\(\Rightarrow F=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)

\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+..+\frac{1}{2008}-\frac{1}{2010}\right)\)

\(\Rightarrow F=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

\(\Rightarrow F=2.\frac{502}{1005}\)

\(\Rightarrow F=\frac{1004}{1005}\)

K=2.(2/2.4+2/4.6+2/6.8+...+2/2008.2010)

K=2.(4-2/2.4+6-4/4.6+8-6/6.8+...+2010-2008/2008.2010)

K=2.(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010)

K=2.(1.2-1.2010)

K=2.502/1005

K=1004/1005

Gọi A= 4/2.4+4/4.6+4/6.8+...+4/2008.2010 
A/2= 2/2.4+2/4.6+...+2/2008.2010 
Mà 2/2.4=1/2-1/4; 2/4.6=1/4-1/6 .... 
Vậy A/2= (1/2-1/4)+(1/4-1/6)+....+(1/2008-1/2010) 
A/2=1/2-1/2010=2010/4020-2/4020=2008/4... 
A= 2008.2/4020=1004/1005

C = 4/2.4 + 4/4.6 + 4/6.8 + ... + 4/2008.2010

C = 2 . (2/2.4 + 2/4.6 + 2/6.8 + ... + 2/2008.2010)

C = 2 . (1/2 - 1/4 + 1/4 - 1/6 + 1/6 - 1/8 + ... + 1/2008 - 1/2010)

C = 2 . (1/2 - 1/2010)

C = 2 . 502/1005

C = 1004/1005

Ta có :

\(F=\dfrac{4}{2.4}+\dfrac{4}{4.6}+..................+\dfrac{4}{2008.2010}\)

\(\Rightarrow F=2\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+.............+\dfrac{2}{2008.2010}\right)\)

\(\Rightarrow F=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+..............+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)

\(\Rightarrow F=2\left(\dfrac{1}{2}-\dfrac{1}{2010}\right)\)

\(\Rightarrow F=2.\dfrac{502}{1005}=\dfrac{1004}{1005}\)

\(F=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+......+\dfrac{4}{2008.2010}\)

\(F=\dfrac{4}{2}\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+.....+\dfrac{1}{2008.2010}\right)\)

\(F=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+.....+\dfrac{1}{2008}-\dfrac{1}{2010}\right)\)\(F=2\left(\dfrac{1}{2}-\dfrac{1}{2010}\right)\)\(F=2.\dfrac{502}{1005}\)

\(F=\dfrac{1004}{1005}\)

A=4/2.4+4/4.6+4/6.8+...+4/2008.2010

=2.(2/2.4+2/4.6+2/6.8+...+2/2008.2010)

=2.(1/2-1/4+1/4-1/6+1/6-1/8+...+1/2008-1/2010)

=2.(1/2-1/2010)

=2.502/1005

=1004/1005

Vậy A=1004/1005

100% giải đúng đầu tiên:

       Ta có: \(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)

                      \(=2.\frac{2}{2.4}+2.\frac{2}{4.6}+2.\frac{2}{6.8}+...+2.\frac{2}{2008.2010}\)

                      \(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+..+\frac{2}{2008.2010}\right)\)

                      \(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

                      \(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)

                       \(=2.\frac{1}{2}-2.\frac{1}{2010}\)

                       \(=1-\frac{1}{1005}=\frac{1004}{1005}\)