4/2.4+4/4.6+...4/2020.2021
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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: \(\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{2018\cdot2020}+\dfrac{4}{2020\cdot2022}\)
\(=2\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{2018\cdot2020}+\dfrac{2}{2020\cdot2022}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{8}+...+\dfrac{1}{2018}-\dfrac{1}{2020}+\dfrac{1}{2020}-\dfrac{1}{2022}\right)\)
\(=2\left(\dfrac{1}{2}-\dfrac{1}{2022}\right)\)
\(=2\cdot\dfrac{505}{1011}\)
\(=\dfrac{1010}{1011}\)
3 tháng 6 2015
\(F=\frac{4}{2.4}+\frac{4}{4.6}+....+\frac{4}{2008.2010}\)
\(F=\frac{4}{2}.\left(\frac{1}{2.4}+\frac{1}{4.6}+....+\frac{1}{2008.2010}\right)\)
\(F=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(F=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{2010}\right)=\frac{4}{2}.\frac{502}{1005}=\frac{1004}{1005}\)
MT
3 tháng 6 2015
F=4/2.4+4/4.6+...+4/2008.2010
=2(2/2.4+2/4.6+....+2/2008.2010)
=2(1/2-1/4+1/4-1/6+....+1/2008-1/2010)
=2(1/2-1/2010)
=2.\(\frac{502}{1005}\)
=\(\frac{8032}{1005}\)
23 tháng 6 2016
A = 4/2 x 4 + 4/4 x 6 + ..... + 4/2008 x 2010
A = 4/2 - 4/4 + 4/4 - 4/6 + ..... + 4/2008 - 4/2010
A = 4/2 - 4/2010
A = Dư bạn ơi !!!!!!!!!!!!!!!!!!
16 tháng 4 2016
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
1 tháng 4 2015
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
19 tháng 6 2016
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
19 tháng 6 2016
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
AM
1 tháng 7 2015
\(A=\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{2014.2016}=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{1015056}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{1007}-\frac{1}{1008}\)
\(=1-\frac{1}{1008}=\frac{1007}{1008}\)
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: \(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(=2.\frac{2}{2.4}+2.\frac{2}{4.6}+2.\frac{2}{6.8}+...+2.\frac{2}{2008.2010}\)
\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+..+\frac{2}{2008.2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2008}-\frac{1}{2010}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{2010}\right)\)
\(=2.\frac{1}{2}-2.\frac{1}{2010}\)
\(=1-\frac{1}{1005}=\frac{1004}{1005}\)
Chúc Em Học Tốt !!
Sửa đề :
\(\frac{4}{2.4}+\frac{4}{4.6}+....+\frac{4}{2020.2022}.\)
= \(2.\left(\frac{2}{2.4}+\frac{2}{4.6}+....+\frac{2}{2020.2022}\right)\)
= \(2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+.....+\frac{1}{2020}-\frac{1}{2022}\right)\)
= \(2.\left(\frac{1}{2}-\frac{1}{2022}\right)\)
= \(2.\frac{505}{1011}\)
= \(\frac{1010}{1011}\)