\(=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2014.2016}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)

\(=2.\frac{1007}{2016}\)

\(=\frac{2007}{1008}\)

giải:

4/2.4+4/4.6+4/6.8+...+4/2012.2014+4/2014.2016

=2.(2/2.4+2/4.6+2/6.8+...+2/2012.2014+2/2014.2016

=2.(1/2-1/4+1,4-1/6+1/6-1/8+...+1/2012-1/2014+1/2014-1/2016)

=2.(1/2-1/2016)

=2.1007/2016

=1007/1008

xong rùi đó

\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2012.2014}+\frac{4}{2014.2016}\)

\(=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2012.2014}+\frac{2}{2014.2016}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)

\(=2.\frac{1007}{2016}\)

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

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{2014}-\frac{1}{2016}\)\(=1-\frac{1}{2016}=\frac{2015}{2016}\)

=1/1x2+1/2x3+1/3x4+...+1/1006x1007+1/1007x1008

=1/1-1/2+1/2-1/3+1/3-1/4+...+1/1006-1/1007+1/1007-1/1008

=1/1-1/1008

=1007/1008

~-~:33

=\(\frac{4}{2}-\frac{4}{4}+\frac{4}{4}-\frac{4}{6}+\frac{4}{6}+....+\frac{4}{2012}-\frac{4}{2014}+\frac{4}{2014}-\frac{4}{2016}\)

= \(\frac{4}{2}-\frac{4}{2016}\)

=\(\frac{1007}{504}\)

hok tốt

      \(\frac{4}{2\cdot4}+\frac{4}{4\cdot6}+\frac{4}{6\cdot8}+...+\frac{4}{2014\cdot2016}\)

\(=2\cdot\left(\frac{2}{2\cdot4}+\frac{2}{4\cdot6}+\frac{2}{6\cdot8}+...+\frac{2}{2014\cdot2016}\right)\)

\(=2\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)

\(=2\cdot\left(\frac{1}{2}-\frac{1}{2016}\right)\)

\(=2\cdot\frac{1007}{2016}\)

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

mình viết nhầm=)))))

\(b,\frac{10}{99}\)+\(\frac{11}{199}\)+\(\frac{12}{299}\).\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{-1}{6}\)

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

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

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

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

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

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

Mình ko ghi lai đề nha

4/2.4/4+4/4.4/6+......+4/2008.4/2010=4/2.4/2010=4/1005

Mình ko bt đúng ko nữa nha 

A x 2/4= 2/2x4 + 2/4x6 + 2/6x8 +............+ 2/2008x2010

A x 2/4=4-2/2x4 + 6-4/4x6 + 8-6/6x8 +.......+ 2010-2008/2008x2010

A x 2/4=4/2x4 - 2/2x4 + 6/4x6 - 4/4x6 +8/6x8 -6/6x8 +............+ 2010/2008x2010 - 2008/2008x2010

A x 2/4=1/2-1/2010

A x 2/4=502/1005

A= 502/1005 / 2/4

A=1004/1005

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

\(C=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2008.2010}\right)\)

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

\(C=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{2010}\right)\) \(;C=\frac{1}{2}.\frac{502}{1005}=\frac{251}{1005}\)

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

=\(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{1004.1005}\)

=\(2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{1004.1005}\right)\)

=\(2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{1004}-\frac{1}{1005}\right)\)

=\(2\left(1-\frac{1}{1005}\right)\)

=\(2.\frac{1004}{1005}\)

=\(\frac{2008}{1005}\)

P/s: Không biết đúng không nữa, làm đại ^.^

Ta thấy : \(\frac{4}{2.4}=\frac{1}{2}\left(\frac{4}{2}-\frac{4}{4}\right);\frac{4}{4.6}=\frac{1}{2}\left(\frac{4}{4}-\frac{4}{6}\right);...;\frac{4}{2008.2010}=\frac{1}{2}\left(\frac{4}{2008}-\frac{4}{2010}\right)\)

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

=> C = \(\frac{1}{2}\left(\frac{4}{2}-\frac{4}{2010}\right)=\frac{1}{2}\left(2-\frac{2}{1005}\right)=\frac{1}{2}\left(\frac{2010}{1005}-\frac{2}{1005}\right)\)

=> C = \(\frac{1}{2}\left(\frac{2010-2}{1005}\right)=\frac{1}{2}.\frac{2008}{1005}=\frac{1004}{1005}\)

K = 4/2 - 4/4 + 4/4 - 4/6 + ....... + 4/2008 - 4/2010

K = 4/2 - 4/2010

K = 4016/2010 = 1/1003/1005

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

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

\(K=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2002}-\frac{1}{2010}\right)\)

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

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

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

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

\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)

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

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

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

Có gì ko hiểu thì cứ hỏi mình nha :)

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

\(=2.2\frac{2}{4}+2.2\frac{2}{4.6}+2.2\frac{2}{6.8}+...+2.2\frac{2}{2008.2010}\)

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

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

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

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

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

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

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

\(\Rightarrow\frac{1}{2}A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{2008.2010}\)

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

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

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

\(\Rightarrow A=\frac{502}{1005}:\frac{1}{2}=\frac{1004}{1005}\)

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

\(\Rightarrow A=4\left(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+.....+\frac{1}{2008.2010}\right)\)

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

\(\Rightarrow A=4\left[\frac{1}{2}\left(\frac{1}{2}-\frac{1}{2010}\right)\right]\Rightarrow A=4\left(\frac{1}{2}.\frac{502}{1005}\right)\Rightarrow A=4.\frac{251}{1005}\Rightarrow A=\frac{1004}{1005}\)

\(B=\frac{1}{18}+\frac{1}{54}+\frac{1}{108}+....+\frac{1}{990}\)

\(\Rightarrow B=\frac{1}{3.6}+\frac{1}{6.9}+\frac{1}{9.12}+....+\frac{1}{30.33}\)

\(\Rightarrow B=\frac{1}{3}\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+.....+\frac{1}{30}-\frac{1}{33}\right)\)

\(\Rightarrow B=\frac{1}{3}.\left(\frac{1}{3}-\frac{1}{33}\right)\Rightarrow B=\frac{1}{3}.\frac{10}{33}\Rightarrow B=\frac{10}{99}\)

= 2(2/2.4 + 2/4.6 +.....+ 2/2008.2016)

= 2(1/2 - 1/4 + 1/4 - 1/6 +....+ 1/2008 - 1/2016)

= 2(1/2 - 1/2016)

=2 . 1007/2016

=1007/1008