\(A=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)
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S
4
H
17 tháng 4 2019
\(D=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)
\(D=\frac{5}{3}.\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)
\(D=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(D=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(D=\frac{5}{3}.\frac{1}{21}\)
\(\Rightarrow D=\frac{5}{63}\)
BD
17 tháng 4 2019
\(3D=3\left(\frac{5}{18\cdot21}+\frac{5}{21\cdot24}+...+\frac{5}{123\cdot126}\right)\)
\(=\frac{3\cdot5}{18\cdot21}+...+\frac{3\cdot5}{123\cdot126}\)
\(=5\left(\frac{3}{18\cdot21}+...+\frac{3}{123\cdot126}\right)\)
\(=5\left(\frac{1}{18}-\frac{1}{21}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(=5\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(=5\left(\frac{7}{126}-\frac{1}{126}\right)\)
\(=5\cdot\frac{6}{126}\)
\(=\frac{30}{126}\)
\(D=\frac{30}{126}\div3=\frac{30}{126}\cdot\frac{1}{3}=\frac{5}{63}\)
\(#Cothanhkhe\)
1 tháng 4 2016
3/5*A=3/(18*21)+3/(21*24)+3/(24*27)+...+3/(123*126)
=>3/5*A=1/18-1/21+1/21-1/24+1/24-1/27+...+1/123-1/126
=>3/5*A=1/18-1/126
=>3/5*A=1/21
=>A=5/63
1 tháng 4 2016
A=\(\frac{5}{3}\left(\frac{3}{18.21}+\frac{3}{21.24}+..........+\frac{3}{123.126}\right)\)
A=\(\frac{5}{3}\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+............+\frac{1}{123}-\frac{1}{126}\right)\)
=\(\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)
=\(\frac{5}{3}.\frac{1}{21}\)
=\(\frac{5}{63}\)
TM
27 tháng 3 2017
\(A=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{5}{123.126}\)
\(A=\frac{5}{3}\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)
\(A=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(A=\frac{5}{3}\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(A=\frac{5}{3}.\frac{1}{21}\)
\(A=\frac{5}{63}\)
MM
1
NT
1
26 tháng 3 2017
\(A=\dfrac{25}{18\cdot21}+\dfrac{25}{21\cdot24}+\dfrac{25}{24\cdot27}+...+\dfrac{25}{123\cdot126}\)
\(=25\left(\dfrac{1}{18\cdot21}+\dfrac{1}{21\cdot24}+\dfrac{1}{24\cdot27}+...+\dfrac{1}{123\cdot126}\right)\)
\(=\dfrac{25}{3}\left(\dfrac{3}{18\cdot21}+\dfrac{3}{21\cdot24}+\dfrac{3}{24\cdot27}+...+\dfrac{3}{123\cdot126}\right)\)
\(=\dfrac{25}{3}\left(\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)
\(=\dfrac{25}{3}\left(\dfrac{1}{18}-\dfrac{1}{126}\right)\)\(=\dfrac{25}{3}\cdot\dfrac{1}{21}=\dfrac{25}{63}\)
MN
26 tháng 3 2017
A= \(\dfrac{25}{18}-\dfrac{25}{21}+\dfrac{25}{21}-\dfrac{25}{24}+...+\dfrac{25}{123}-\dfrac{25}{126}\)
A= \(\dfrac{25}{18}-\dfrac{25}{126}\)
A= \(\dfrac{25}{21}\)
Hoặc ngay dòng 2 bạn làm như thế này cũng được: \(25.\left(\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{123}-\dfrac{1}{126}\right)\)
30 tháng 6 2018
A = 54/15.18 + 54/18.21 + .........+ 54/87.90
A = 54/3 . ( 1/15.18 + 1/18.21 + ........+ 1/87.90)
A = 54/3 . ( 1/15 - 1/18 + 1/18 -1/21 + ......+ 1/87 - 1/90)
A =54/3 . ( 1/15 -1/90)
A = 54/3 . 1/18 = 1
vậy A = 1
KD
26 tháng 8 2016
D=\(\frac{6}{15.18}\)+\(\frac{6}{18.21}\)+...+\(\frac{6}{87.90}\)
D=2.\(\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)
D=2.\(\frac{1}{18}\)
D=\(\frac{1}{9}\)
Vậy D=\(^{\frac{1}{9}}\)
26 tháng 8 2016
\(D=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)
\(D=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)
\(D=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(D=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(D=2.\left(\frac{6}{90}-\frac{1}{90}\right)\)
\(D=2.\frac{1}{18}\)
\(D=\frac{1}{9}\)
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
31 tháng 10 2017
a/
\(1995^n.1997^n=\left(1995.1997\right)^n\)
\(1996^{2n}=\left(1996^2\right)^n\)
\(1995.1997=\left(1996-1\right).\left(1996+1\right)=1996^2-1\)
\(\Rightarrow1995.1997< 1996^2\Rightarrow1995^n.1997^n< 1996^{2n}\)
b/
\(A=\frac{1}{2.9}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{9.20}+\frac{1}{9.30}+\frac{1}{9.42}+\frac{1}{9.56}\)
\(A=\frac{1}{9}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)\)
\(A=\frac{1}{9}\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{8-7}{7.8}\right)\)
\(A=\frac{1}{9}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\right)\)
\(A=\frac{1}{9}\left(1-\frac{1}{9}\right)=\frac{1}{9}.\frac{8}{9}=\frac{8}{81}\)
A= \(\frac{5}{3}\)(\(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...\frac{3}{123.126}\)
A=\(\frac{5}{3}\)(\(\frac{1}{18}-\frac{1}{126}\))
A=\(\frac{5}{3}.\frac{1}{21}\)
A=\(\frac{5}{63}\)
\(A=\frac{5}{18.21}+\frac{5}{21.24}+\frac{5}{24.27}+...+\frac{4}{123.126}\)
\(=\frac{5}{3}.\left(\frac{3}{18.21}+\frac{3}{21.24}+\frac{3}{24.27}+...+\frac{3}{123.126}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{123}-\frac{1}{126}\right)\)
\(=\frac{5}{3}.\left(\frac{1}{18}-\frac{1}{126}\right)\)
\(=\frac{5}{3}.\frac{1}{21}\)
\(=\frac{5}{63}\)