Sửa đề: \(\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{2018\cdot2020}+\dfrac{4}{2020\cdot2022}\)

Ta có: \(\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{2018\cdot2020}+\dfrac{4}{2020\cdot2022}\)

\(=2\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{2018\cdot2020}+\dfrac{2}{2020\cdot2022}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2018}-\dfrac{1}{2020}+\dfrac{1}{2020}-\dfrac{1}{2022}\right)\)

\(=2\left(\dfrac{1}{2}-\dfrac{1}{2022}\right)\)

\(=2\cdot\dfrac{505}{1011}\)

\(=\dfrac{1010}{1011}\)

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

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

F=2/2-2/4+2/4-2/6+2/6-2/8+......+2/2008-2/2010

F=2/2- 2/4+2/4-2/6+2/6-2/8+......+2/2008-2/2010

F=2/2-2/2010

=>F=2008/2010=1004/1005

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

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

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

\(A=\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{2014.2016}=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{1015056}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{1007}-\frac{1}{1008}\)

\(=1-\frac{1}{1008}=\frac{1007}{1008}\)

4/2-4/4+4/4-4/6+....+4/2014-4/2015

=4/2-4/2015

=2-4/2015

= 4030-4/2015

=4026/2015

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

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

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

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

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

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

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

a)   \(\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+\frac{1}{8\cdot10}\)

\(=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}\right)\)

\(=\frac{1}{2}\cdot\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{5}=\frac{2}{10}=\frac{1}{5}\)

b)   \(\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}\)

\(=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}\)

\(=1-\frac{1}{17}=\frac{16}{17}\)

hok tốt ...

a)\(A=\frac{1}{2\cdot4}+\frac{1}{4\cdot6}+\frac{1}{6\cdot8}+\frac{1}{8\cdot10}\)

\(2A=\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+\frac{2}{8\cdot10}\)

\(2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}=\frac{1}{2}-\frac{1}{10}=\frac{2}{5}\)

\(A=\frac{2}{5}\cdot\frac{1}{2}=\frac{1}{5}\)

b)\(B=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+\frac{4}{9\cdot13}+\frac{4}{13\cdot17}=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}=1-\frac{1}{17}=\frac{16}{17}\)

a) 1/2.4 + 1/4.6 + 1/6.8 + 1/8.10

= 2/2.2.4 + 2/2.4.6 + 2/2.6.8 + 2/2.8.10 ( nhân cả tử và mẫu với 2)

= 1/2 .( 2/2.4 + 2/4.6 + 2/6.8 + 2/8.10 )

= 1/2 .(1/2 - 1/4 + 1/4 - 1/8 + 1/8 - 1/10)

= 1/2.(1/2 - 1/10)

= 1/2.( 5/10 - 1/10) = 1/2.4/10 = 2/10 = 1/5

b) 4/1.5+ 4/5.9 + 4/ 9.13 + 4/13.17

= 1- 1/5 + 1/5 - 1/9 + 1/9 - 1/13 + 1/13 - 1/17

= 1- 1/17

= 16/17 

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