K
Khách
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28 tháng 1 2022
\(K=\dfrac{5}{4}\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{85}-\dfrac{1}{89}\right)\)
\(=\dfrac{5}{4}\cdot\left(\dfrac{1}{3}-\dfrac{1}{89}\right)=\dfrac{5}{4}\cdot\dfrac{86}{267}=\dfrac{215}{534}\)
17 tháng 2 2015
a=4/3.7 +4/7.11+4/11.15 +.....+4/107/111
=1/3-1/7+1/7-1/11+1/11-1/15+......+1/107-1/111
=1/3-1/111
=12/37
NA
1
KV
19 tháng 8 2023
\(\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+...+\dfrac{4}{59.63}\)
\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{59}-\dfrac{1}{63}\)
\(=\dfrac{1}{3}-\dfrac{1}{63}\)
\(=\dfrac{20}{63}\)
NP
1
HT
2 tháng 9 2015
A = \(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{95.99}\)
A = \(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{99}\)
A = \(\frac{1}{3}-\frac{1}{99}\)
A = \(\frac{32}{99}\)
L
3
15 tháng 7 2017
\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{23.27}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}+0+0+0+0\)
\(=\frac{8}{27}\)
15 tháng 7 2017
Ta có : \(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+\frac{4}{23.27}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+.....+\frac{1}{23}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}\)
\(=\frac{8}{27}\)
NL
2
HN
5 tháng 5 2016
\(A=\frac{4^2}{3.7}+\frac{4^2}{7.11}+\frac{4^2}{11.15}+...+\frac{4^2}{107.111}\)
\(A=\) \(4\left(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{107.111}\right)\)
\(A=4\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\right)\)
\(A=4\left(\frac{1}{3}-\frac{1}{111}\right)\)
\(A=4.\frac{12}{37}\)
\(A=\frac{48}{37}\)
TN
19 tháng 8 2016
\(A=\frac{4}{3.7}+\frac{4}{7.11}+....+\frac{4}{95.99}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{95}-\frac{1}{99}\)
\(=\frac{1}{3}-\frac{1}{99}\)
\(=\frac{32}{99}\)
KB
6
NB
11 tháng 3 2015
Ta thấy \(\frac{1}{3}-\frac{1}{7}=\frac{7-3}{3.7}=\frac{4}{3.7}\)
\(\frac{1}{7}-\frac{1}{11}=\frac{11-7}{7.11}=\frac{4}{7.11}\)
..........................
\(\frac{1}{1023}-\frac{1}{1027}=\frac{1027-1023}{1023.1027}=\frac{4}{1023.1027}\)
=> \(\frac{4}{3.7}+\frac{4}{7.11}+....+\frac{4}{1023.1027}=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+....+\frac{1}{1023}-\frac{1}{1027}\)
=> =\(\frac{1}{3}-\frac{1}{1027}=\frac{1024}{3.1027}\)
QN
14 tháng 7 2017
Ta có: \(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{1023.1027}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{1023}-\frac{1}{1027}\)
\(=\frac{1}{3}-\frac{1}{1027}=\frac{1024}{3081}\)
14 tháng 3 2016
4x(\(\frac{1}{3.7}+...+\frac{1}{107.111}\) )
4(\(\frac{1}{3}-\frac{1}{7}+...+\frac{1}{107}-\frac{1}{111}\))
4(\(\frac{1}{3}-\frac{1}{111}\))
4.\(\frac{12}{37}\)
48/37
LP
1
BM
21 tháng 3 2016
Ta có A = \(\frac{4}{3.7}+\frac{4}{7.11}+..............+\frac{4}{107.111}\)
=> A = \(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+.............+\frac{1}{107}-\frac{1}{111}\)
A = \(\frac{1}{3}-\frac{1}{111}=\frac{12}{37}\)
k nha bạn
ta có :
\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+..+\frac{4}{85.89}\)
\(=\frac{7-3}{3.7}+\frac{11-7}{7.11}+...+\frac{89-85}{85.89}=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+..+\frac{1}{85}-\frac{1}{89}=\frac{1}{3}-\frac{1}{89}\)
\(=\frac{86}{267}\)
4/3.7+4/7.11+4/11.15+...+4/85.89
=1/3-1/7+1/7-1/11+1/11-1/15+...+1/85-1/89
=1/3-1/89
=86/267