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NQ
0
PC
3
TG
23 tháng 5 2021
\(N=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2014.2016}\)
\(=2\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+\dfrac{2}{6.8}+...+\dfrac{2}{2014.2016}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2014}-\dfrac{1}{2016}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{2016}\right)\)
\(=2\left(\dfrac{1008}{2016}-\dfrac{1}{2016}\right)\)
\(=2.\dfrac{1007}{2016}=\dfrac{1007}{1008}\)
23 tháng 5 2021
Công thức đây bạn:
\(\dfrac{a}{n\left(n+a\right)}=\dfrac{1}{n}-\dfrac{1}{n+a}\)
PN
1
30 tháng 3 2016
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!
PT
9
4 tháng 8 2016
\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+....+\frac{4}{2014.2016}\)
\(=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{2014.2016}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+.....+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(=2.\frac{1007}{2016}=\frac{1007}{1008}\)
LH
4 tháng 8 2016
\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2014.2016}\)
\(A=\frac{4}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2014.2016}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{2016}\right)=2.\frac{1007}{2016}=\frac{1007}{1008}\)
20 tháng 4 2019
\(=2.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{2014.2016}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(=2.\frac{1007}{2016}\)
\(=\frac{2007}{1008}\)
KT
20 tháng 4 2019
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
TD
1
13 tháng 4 2016
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.......+\frac{1}{2014}-\frac{1}{2016}\)\(=1-\frac{1}{2016}=\frac{2015}{2016}\)
PC
5
23 tháng 5 2021
\(N=\frac{4}{2.4}+\frac{4}{4.6}+..+\frac{4}{2014.2016}\)
\(N=\frac{4}{2}\left(\frac{1}{2.4}+\frac{1}{4.6}+..+\frac{1}{2014.2016}\right)\)
\(N=2\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(N=\frac{2}{2}-\frac{2}{2016}=1-\frac{2}{2016}\)
\(N=\frac{2014}{2016}\)
Bn bấm máy rút gọn nhé
S
9 tháng 5 2019
=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
29 tháng 4 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
29 tháng 4 2015
100% giải đúng đầu tiên:
Ta có: \(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(=2.\frac{2}{2.4}+2.\frac{2}{4.6}+2.\frac{2}{6.8}+...+2.\frac{2}{2008.2010}\)
\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+..+\frac{2}{2008.2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(=2.\frac{1}{2}-2.\frac{1}{2010}\)
\(=1-\frac{1}{1005}=\frac{1004}{1005}\)
NT
1
29 tháng 4 2021
Sửa đề: \(\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{2018\cdot2020}+\dfrac{4}{2020\cdot2022}\)
Ta có: \(\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{2018\cdot2020}+\dfrac{4}{2020\cdot2022}\)
\(=2\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{2018\cdot2020}+\dfrac{2}{2020\cdot2022}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2018}-\dfrac{1}{2020}+\dfrac{1}{2020}-\dfrac{1}{2022}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{2022}\right)\)
\(=2\cdot\dfrac{505}{1011}\)
\(=\dfrac{1010}{1011}\)
Ta có:
A=4/2(2/2.4+2/4.6+...+2/2014.2016)
A=4/2(1/2-1/4+1/4-1/6+...+1/2014-1/2016)
A=4/2(1/2-1/2016)
A=4/2.1007/2016
=>A=1007/1008
\(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2014.2016}\)
\(A=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2014}-\frac{1}{2016}\right)\)
\(A=2.\left(\frac{1}{2}-\frac{1}{2016}\right)\)
\(A=2.\frac{1007}{2016}\)
\(A=\frac{1007}{1008}\)