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Đặt \(A=\frac{3}{5.11}+\frac{5}{11.21}+\frac{7}{21.35}+\frac{9}{35.53}\)
\(2A=\frac{6}{5.11}+\frac{10}{11.21}+\frac{14}{21.35}+\frac{18}{35.53}\)
\(2A=\frac{1}{5}-\frac{1}{11}+\frac{1}{11}-\frac{1}{21}+\frac{1}{21}-\frac{1}{35}+\frac{1}{35}-\frac{1}{53}\)
\(2A=\frac{1}{5}-\frac{1}{53}\)
\(2A=\frac{48}{265}\)
\(A=\frac{48}{265}:2\)
\(A=\frac{24}{265}\)
Vì \(\frac{24}{265}< 1\)nên \(A< 1\)(Điều phải chứng tỏ)
Ủng hộ mk nha !!! ^_^
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Ta có:
\(\dfrac{1}{5}>\dfrac{1}{10}\\ \dfrac{1}{6}>\dfrac{1}{10}\\ ...\\ \dfrac{1}{9}>\dfrac{1}{10}\\ \Rightarrow\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{9}>\dfrac{5}{10}=\dfrac{1}{2}.\)
Tương tự:
\(\dfrac{1}{10}+\dfrac{1}{11}+...+\dfrac{1}{14}>\dfrac{5}{15}=\dfrac{1}{3}.\\ \dfrac{1}{15}+\dfrac{1}{16}+\dfrac{1}{17}>\dfrac{3}{18}=\dfrac{1}{6}.\)
Cộng vế theo vế ta được \(B>\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}=1\left(đpcm\right)\)
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`@` `\text {Ans}`
`\downarrow`
`a)`
\(\dfrac{7}{5}\cdot\dfrac{8}{19}+\dfrac{7}{5}\cdot\dfrac{12}{19}-\dfrac{7}{5}\cdot\dfrac{1}{19}\)
`=`\(\dfrac{7}{5}\cdot\left(\dfrac{8}{19}+\dfrac{12}{19}-\dfrac{1}{19}\right)\)
`=`\(\dfrac{7}{5}\cdot\dfrac{19}{19}=\dfrac{7}{5}\cdot1=\dfrac{7}{5}\)
`b)`
\(-\dfrac{3}{5}\cdot\dfrac{5}{7}+\left(-\dfrac{3}{5}\right)\cdot\dfrac{3}{7}+\left(-\dfrac{3}{5}\right)\cdot\dfrac{6}{7}\)
`=`\(-\dfrac{3}{5}\cdot\left(\dfrac{5}{7}+\dfrac{3}{7}+\dfrac{6}{7}\right)\)
`=`\(-\dfrac{3}{5}\cdot\dfrac{14}{7}\)
`=`\(-\dfrac{3}{5}\cdot2=-\dfrac{6}{5}\)
`c)`
\(10\dfrac{2}{9}+\left(2\dfrac{2}{5}-7\dfrac{2}{9}\right)\)
`=`\(10\dfrac{2}{9}+2\dfrac{2}{5}-7\dfrac{2}{9}\)
`=`\(\left(10\dfrac{2}{9}-7\dfrac{2}{9}\right)+2\dfrac{2}{5}\)
`=`\(3+2\dfrac{2}{5}=\dfrac{27}{5}\)
`d)`
\(6\dfrac{3}{10}-\left(3\dfrac{4}{7}+2\dfrac{3}{10}\right)\)
`=`\(6\dfrac{3}{10}-3\dfrac{4}{7}-2\dfrac{3}{10}\)
`=`\(\left(6\dfrac{3}{10}-2\dfrac{3}{10}\right)-3\dfrac{4}{7}\)
`=`\(4-3\dfrac{4}{7}=\dfrac{3}{7}\)
a) \(\dfrac{7}{5}.\dfrac{8}{19}+\dfrac{7}{5}.\dfrac{12}{19}-\dfrac{7}{5}.\dfrac{1}{19}\)
\(=\dfrac{7}{5}.\left(\dfrac{8}{19}+\dfrac{12}{19}-\dfrac{1}{19}\right)\)
\(=\dfrac{7}{5}.1\)
\(=\dfrac{7}{5}\)
b) \(\dfrac{-3}{5}.\dfrac{5}{7}+\dfrac{-3}{5}.\dfrac{3}{7}+\dfrac{-3}{5}.\dfrac{6}{7}\)
\(=\dfrac{-3}{5}.\left(\dfrac{5}{7}+\dfrac{3}{7}+\dfrac{6}{7}\right)\)
\(=\dfrac{-3}{5}.2\)
\(=\dfrac{-6}{5}\)
c) \(10\dfrac{2}{9}+\left(2\dfrac{2}{5}-7\dfrac{2}{9}\right)\)
\(=\dfrac{92}{9}+\dfrac{12}{5}-\dfrac{65}{9}\)
\(=\dfrac{92}{9}-\dfrac{65}{9}+\dfrac{12}{5}\)
\(=3+\dfrac{12}{5}\)
\(=\dfrac{15}{5}+\dfrac{12}{5}\)
\(=\dfrac{27}{5}\)
d) \(6\dfrac{3}{10}-\left(3\dfrac{4}{7}+2\dfrac{3}{10}\right)\)
\(=\dfrac{63}{10}-\dfrac{25}{7}-\dfrac{23}{10}\)
\(=\dfrac{63}{10}-\dfrac{23}{10}-\dfrac{25}{7}\)
\(=4-\dfrac{25}{7}\)
\(=\dfrac{28}{7}-\dfrac{25}{7}\)
\(=\dfrac{3}{7}\)
Chúc bạn học tốt
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1+2+...+99\(=\frac{99.100}{2}=99.50=2.3^2.5.11\) chia hết cho 2,3,5,9.
![](https://rs.olm.vn/images/avt/0.png?1311)
10^9 + 10^8 + 10^7 = 10^6 x (10^3 + 10^2 + 10) = 10^6 x 111
10^6 chia hết cho 5
-> 10^6 x 111 chia hết cho 5 x 111
hay 10^6 x 111 chia hết cho 555
Vậy 10^9 + 10^8 + 10^ 7 chia hết cho 555
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Leftrightarrow n+1\in\left\{1;3\right\}\)
hay \(n\in\left\{0;2\right\}\)
mình đang cần gấp lắm
Ta thấy rằng:
Phân số: 3/5 là phân số nhỏ hơn 1
5/11 < 1
7/21 < 1
9/35 < 1
Và 3/11 < 1
5/21 < 1
7/35 < 1
9/53 < 1
Tất cả phân số đều nhỏ hơn 1
= > Phép tính trên nhỏ hơn 1