1x4+7-9=?
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ND
2
DP
12 tháng 7 2017
Đặt \(A=\frac{3}{1\cdot4}+\frac{5}{4\cdot9}+\frac{7}{9\cdot16}+\frac{9}{16\cdot25}+\frac{11}{25\cdot36}\)
\(A=\frac{4-1}{1\cdot4}+\frac{9-4}{4\cdot9}+\frac{16-9}{9\cdot16}+\frac{25-16}{16\cdot25}+\frac{36-25}{25\cdot36}\)
\(A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{16}+\frac{1}{16}-\frac{1}{25}+\frac{1}{25}-\frac{1}{36}\)
\(\Rightarrow A=1-\frac{1}{36}=\frac{35}{36}\)
12 tháng 7 2017
= 1-\(\frac{1}{4}\)+ \(\frac{1}{4}\)-\(\frac{1}{9}\)+\(\frac{1}{9}\)-\(\frac{1}{16}\)+\(\frac{1}{16}\)-\(\frac{1}{25}\)+\(\frac{1}{25}\)-\(\frac{1}{36}\)=1-\(\frac{1}{36}\)=35/36
MC
18 tháng 7 2021
\(-\frac{12}{35}\div\frac{7}{11}-\frac{23}{35}\div\frac{7}{11}-\frac{5}{11}\)
\(=\left(-\frac{12}{35}-\frac{23}{35}\right)\div\frac{7}{11}-\frac{5}{11}\)
\(=-1\div\frac{7}{11}-\frac{5}{11}\)
\(=-\frac{11}{7}-\frac{5}{11}\)
\(=-\frac{156}{77}\)
29 tháng 8 2023
\(A=\dfrac{7}{1.9}+\dfrac{7}{9.17}+\dfrac{7}{17.25}+...+\dfrac{7}{81.89}\)
\(\dfrac{8}{7}A=\dfrac{8}{1.9}+\dfrac{8}{9.17}+\dfrac{8}{17.25}+...+\dfrac{8}{81.89}\)
\(\dfrac{8}{7}A=1-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{25}+...+\dfrac{1}{81}-\dfrac{1}{89}\)
\(\dfrac{8}{7}A=1-\dfrac{1}{89}=\dfrac{88}{89}\Rightarrow A=\dfrac{88}{89}:\dfrac{8}{7}=\dfrac{77}{89}\)
\(B=\dfrac{5^2}{1.4}+\dfrac{3^2}{4.7}+\dfrac{3^2}{7.10}+...+\dfrac{3^2}{37.40}\)
\(B=\dfrac{25}{1.4}+\dfrac{9}{4.7}+\dfrac{9}{7.10}+...+\dfrac{9}{37.40}\)
\(\dfrac{1}{3}B=\dfrac{25}{12}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{37.40}\)
\(\dfrac{1}{3}B=\dfrac{25}{12}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{37}-\dfrac{1}{40}\)
\(\dfrac{1}{3}B=\dfrac{25}{12}+\dfrac{1}{4}-\dfrac{1}{40}=\dfrac{277}{120}\Rightarrow B=\dfrac{277}{120}:\dfrac{1}{3}=\dfrac{277}{40}\)
29 tháng 8 2023
\(A=\dfrac{7}{1.9}+\dfrac{7}{9.17}+\dfrac{7}{17.25}+...+\dfrac{7}{81.89}\)
\(=7\left(\dfrac{8}{1.9}+\dfrac{8}{9.17}+\dfrac{8}{17.25}+...+\dfrac{8}{81.89}\right)\)
\(=7\left(1-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{25}+\dfrac{1}{25}+...+\dfrac{1}{81}-\dfrac{1}{89}\right)\)
\(=7.\left(1-\dfrac{1}{89}\right)=7.\dfrac{88}{89}=\dfrac{616}{89}\)
26 tháng 9 2021
\(\dfrac{m}{n}=\dfrac{7}{1\cdot4}+\dfrac{7}{4\cdot7}+...+\dfrac{7}{37\cdot40}\)
\(=\dfrac{7}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{37\cdot40}\right)\)
\(=\dfrac{7}{3}\left(1-\dfrac{1}{40}\right)\)
\(=\dfrac{7}{3}\cdot\dfrac{39}{40}=\dfrac{91}{40}\)
\(\Leftrightarrow\left(m,n\right)=\left(91;40\right)\)
Suy ra: S=91+40=131
KO
21 tháng 4 2016
S=3/1.4+3/4.7+3/7.10+.....+3/40.43+3/43.46
S= 1/1-1/4+1/4-1/7+1/7-1/10+...+1/40-1/43+1/43-1/46
S= 1-1/46
=> S<1
24 tháng 4 2016
S=3.(1/1-1/4+1/4-1/7+.........+1/40-1/43+1/43-1/46)
S=3.(1/1-1/46)
S=3.45/46
S=2/43/46
=> 2/43/46>1
=>S>1
=2 nha
1 x 4 + 7 - 9
= 4 + 7 - 9
= 11 - 9
= 2