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

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

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

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

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

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

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

=> K : 2 = \(\frac{2}{2.4}+\frac{2}{4.6}+....+\frac{2}{2008.2010}\)

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

            =\(\frac{1}{2}-\frac{1}{2010}=\frac{502}{1005}\)

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

Vậy \(K=\frac{1004}{1005}\)

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)

:D thầy ra đề cương khó quá nên các bạn giúp mình với!!!!!

S = \(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2016.2018}\)

S = \(2.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2016.2018}\right)\)

S = \(2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2016}-\frac{1}{2018}\right)\)

S = \(2.\left(\frac{1}{2}-\frac{1}{2018}\right)\)

S = \(2.\frac{504}{1009}\)= \(\frac{1008}{1009}\)

Vậy S = \(\frac{1008}{1009}\).

~~~

Nếu có sai sót gì thì giúp đỡ tớ nha :3

#Sunrise

Cảm ơn Lê Cao Mai Anh nhìu lắm

a) =1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101

    =1-1/101

    =100/101

b) =(2/1.3+2/3.5+2/5.7+...+2/99.101).2,5

    =(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101).2,5

    =(1-1/101).2,5

    =100/101.2,5

    =250/101

c) =(2/2.4+2/4.6+2/6.8+...+2/2008-2/2010).2

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

    =(1/2-1/2010).2

    =1004/1005

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

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

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

K = 2 . 1004/2010

K = 1004/1005

Ai k mk mk k lại 

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

K=\(\frac{4}{2}.\frac{2}{2.4}+\frac{4}{2}.\frac{2}{4.6}+...+\frac{4}{2}.\frac{2}{2008.2010}\)

K=\(\frac{4}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2008.2010}\right)\)

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

K=\(\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{2010}\right)\)

K=\(\frac{4}{2}.\frac{502}{1005}\)

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

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

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

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

\(K=2\times\frac{502}{1005}\)

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