\(N=\frac{4}{2.4}+\frac{4}{4.6}+..+\frac{4}{2014.2016}\)

\(N=\frac{4}{2}\left(\frac{1}{2.4}+\frac{1}{4.6}+..+\frac{1}{2014.2016}\right)\)

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

\(N=\frac{2}{2}-\frac{2}{2016}=1-\frac{2}{2016}\)

\(N=\frac{2014}{2016}\)

Bn bấm máy rút gọn nhé

cho mik xin công thức tính dc như thế

Bạn nhắn tin mk chỉ cho nhé

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

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

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

=4/2-4/2015

=2-4/2015

= 4030-4/2015

=4026/2015

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\(=2.\frac{1007}{2016}=\frac{1007}{1008}\)

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

\(A=\frac{4}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2014.2016}\right)\)

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

\(A=2\left(\frac{1}{2}-\frac{1}{2016}\right)=2.\frac{1007}{2016}=\frac{1007}{1008}\)

A = 4/2.4 + 4/4.6 + 4/6.8 + ... + 4/2014.2016

A = 2.(2/2.4 + 2/4.6 + 2/6.8 + ... + 2/2014.2016)

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

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

A = 2.1/2 - 2.1/2016

A = 1 - 1/1008

A = 1007/1008

B = 1/18 + 1/54 + 1/108 + ... + 1/990

B = 1/9.(1/2 + 1/6 + 1/12 + ... + 1/110)

B = 1/9.(1/1.2 + 1/2.3 + 1/3.4 + ... + 1/10.11)

B = 1/9.(1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/10 - 1/11)

B = 1/9.(1 - 1/11)

B = 1/9.10/11

B = 10/99

F = 2.(2/2.4 + 2/4.6 +......+ 2/2014.2016)

F = 2.(1/2 - 1/4 + 1/4 - 1/6 +.......+1/2014 - 1/2016)

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

F = 2 . 1007/2016

F = 2014/2016

Ủng hộ nhé!

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

=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 ko chép lại đề nhé, sửa 2014 + 2016 thành 2014.2016

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

\(=2\left(\dfrac{1}{2}-\dfrac{1}{2016}\right)=2\left(\dfrac{2016-2}{6032}\right)=\dfrac{2.2018}{6032}=\dfrac{4036}{6032}=\dfrac{1009}{1508}\)

\(A=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2014.2016}\)

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

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

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

\(=2.\dfrac{1007}{2016}=\dfrac{1007}{1008}\)

Giải:

Sửa đề 4/2014+2016 ➜ 4/2014.2016

A=4/2.4+4/4.6+4/6.8+...+4/2014.2016

A=2.(2/2.4+2/4.6+2/6.8+...+2/2014.2016)

A=2.(2/2-2/4+2/4-2/6+2/6-2/8+...+2/2014-2/2016)

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

A=2.1007/1008

A=1007/504

Chúc bạn học tốt!