B=2/11x15 2/15x19 2/19x23 ... 2/51x55
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MT
1 tháng 7 2015
B=2/11x15+2/15x19+2/19x23+...+2/51x55
=>2B=4/11x15+4/15x19+4/19x23+...+4/51x55
=1/11-1/15+1/15-1/19+...+1/51-1/55
=1/11-1/55
=5/55-1/55
=4/55
=>B=4/55 : 2
=4/55.1/2
=2/55
1 tháng 7 2015
\(B=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+...+\frac{1}{51}-\frac{1}{55}\right)\)
\(B=\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{1}{2}.\frac{4}{55}=\frac{2}{55}\)
M
20 tháng 3 2018
\(C=\frac{2}{11.15}+\frac{2}{15.19}+\frac{2}{19.13}+...+\frac{2}{51.55}\)
\(2.C=\frac{4}{11.15}+\frac{4}{15.19}+\frac{4}{19.23}+...+\frac{4}{51.55}\)
\(2.C=\frac{1}{11}-\frac{1}{15}+\frac{1}{15}-\frac{1}{19}+\frac{1}{19}-\frac{1}{23}+...+\frac{1}{51}-\frac{1}{55}\)
\(2.C=\frac{1}{11}-\frac{1}{55}\)
\(2.C=\frac{5}{55}-\frac{1}{55}=\frac{4}{55}\)
\(C=\frac{4}{55}:2=\frac{4}{55}.\frac{1}{2}=\frac{2}{55}\)
Vậy \(C=\frac{2}{55}\)
TV
2
24 tháng 3 2021
ta có:
A=2/4(4/11.15+4/15.19+4/19.23+.....+4/51.55)
A=2/4(1/11-1/15+1/15-1/19+1/19-1/23+....+1/51-1/55)
A=2/4(1/11-1/55)
A=2/4*4/55=8/220=2/55
B=-55/3/*8/3=-165/24=-55/8
suy ra A*B=2/55*(-55/8)=-1/4
TA
1
23 tháng 2 2023
SỬa đề: \(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+...+\dfrac{4}{23\cdot27}\)
\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{23}-\dfrac{1}{27}\)
=1/3-1/27
=8/27
HD
2
S
14 tháng 2 2023
\(A=\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+\dfrac{4}{15.19}+\dfrac{4}{19.23}+\dfrac{4}{23.27}\)(Dấu . là dấu nhân)
\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{27}\)
\(=\dfrac{1}{3}-\dfrac{1}{27}\)
\(=\dfrac{9}{27}-\dfrac{1}{27}\)
\(=\dfrac{8}{27}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
14 tháng 2 2023
A = 4/3x7 + 4/7x11+ 4/11x15 + 4/15x19 + 4/19 x23 + 4/23 x 27
A = 1/3-1/7+1/7-1/11+1/11-1/15+1/15-1/19+1/19-1/23+1/23 -1/27
A = 1/3 - 1/27
A = 8/27
Y
29 tháng 6 2017
Ta có :
\(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+....+\frac{4}{23.27}\)
\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+....+\frac{1}{23}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}==\frac{9}{27}-\frac{1}{27}=\frac{8}{27}\)
DA
16 tháng 8 2017
a)\(A=\frac{2}{3}+\frac{2}{6}+\frac{2}{12}+\frac{2}{24}+\frac{2}{48}+\frac{2}{96}+\frac{2}{192}\)
\(\frac{1}{2}xA=\frac{1}{3}+\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}\)
\(\frac{1}{4}xA=\frac{1}{6}+\frac{1}{12}+\frac{1}{24}+\frac{1}{48}+\frac{1}{96}+\frac{1}{192}+\frac{1}{384}\)
\(\frac{1}{4}xA-\frac{1}{2}xA=\frac{1}{3}-\frac{1}{384}\)
\(\frac{1}{4}xA=\frac{127}{384}\)
\(A=\frac{127}{384}:\frac{1}{4}\)
\(A=\frac{127}{96}\)
KT
15 tháng 10 2018
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)
\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=9-\left(1-\frac{1}{10}\right)\)
\(=9-\frac{9}{10}=\frac{81}{10}\)
TH1)
\(B=\dfrac{2}{11x15}+\dfrac{2}{15x19}+\dfrac{2}{19x23}+......+\dfrac{2}{51x55}\)
\(B=\dfrac{2}{11}-\dfrac{2}{15}+\dfrac{2}{15}-\dfrac{2}{19}+\dfrac{2}{19}-\dfrac{2}{23}+.....+\dfrac{2}{51}-\dfrac{2}{55}\)
\(B=\dfrac{2}{11}-\dfrac{2}{55}\)
\(B=\dfrac{8}{55}\)
TH2)
\(B=\dfrac{2}{11x15}-\dfrac{2}{15x19}-\dfrac{2}{19x23}-......-\dfrac{2}{51x55}\)
\(B=\dfrac{2}{11}+\dfrac{2}{15}-\dfrac{2}{15}+\dfrac{2}{19}-\dfrac{2}{19}+\dfrac{2}{23}-....-\dfrac{2}{51}+\dfrac{2}{55}\)
\(B=\dfrac{2}{11}+\dfrac{2}{55}\)
\(B=\dfrac{12}{55}\)