4/9.12+4/12.15+...+4/270.273
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\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{9}+...+\dfrac{1}{15}-\dfrac{1}{18}\right)\)
\(=\dfrac{1}{3}\left(\dfrac{1}{3}-\dfrac{1}{18}\right)=\dfrac{1}{3}\cdot\dfrac{5}{18}=\dfrac{5}{54}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=9.12+12.15+15.18-18.21
A=9.12+(12.15+15.18)-18.21
A=9.12+15.(12+18)-18.21
A=9.12+15.40-18.21
Vì 9.12 +15.40-18.21 chia hết cho2,3,,5,6,10,15
suy r a CHIA HÊT CHO 2,3,5,6,10,15
B tuong tự
k nhá Huyền hâm. tao nhắc cho mày rồi đấy nhá.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{4}{3.6}+\frac{4}{6.9}+...+\frac{4}{12.15}\)
\(=\frac{4\left(\frac{3}{3.6}+\frac{3}{6.9}+...+\frac{3}{12.15}\right)}{3}\)
\(=\frac{4\left(\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{9}+...+\frac{1}{12}-\frac{1}{15}\right)}{3}\)
\(=\frac{4\left(\frac{1}{3}-\frac{1}{15}\right)}{3}\)
\(=\frac{\frac{16}{15}}{3}=\frac{48}{15}\)
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\(4^{11}.25^{11}\le2^n.5^n\le20^{12}.5^{12}\)
\(\Rightarrow\left(4.25\right)^{11}\le\left(2.5\right)^n\le\left(20.5\right)^{12}\)
\(\Rightarrow100^{11}\le10^n\le100^{12}\)
\(\Rightarrow10^{110}\le10^n\le10^{120}\)
\(\Rightarrow n\in\left\{110;111;...;120\right\}\)
Mk sửa đề chút nhé nếu đề của mk k đúng thì bạn có thể thay đổi cách làm để làm bài của bạn nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
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/
\(A=\frac{1}{2.9}+\frac{1}{6.9}+\frac{1}{9.12}+\frac{1}{9.20}+\frac{1}{9.30}+\frac{1}{9.42}+\frac{1}{9.56}\)
\(A=\frac{1}{9}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\right)\)
\(A=\frac{1}{9}\left(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{8-7}{7.8}\right)\)
\(A=\frac{1}{9}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}\right)\)
\(A=\frac{1}{9}\left(1-\frac{1}{9}\right)=\frac{1}{9}.\frac{8}{9}=\frac{8}{81}\)
\(A=\frac{4}{9.12}+\frac{4}{12.15}+...+\frac{4}{270.273}\)
\(A=\frac{4}{3}\left(\frac{3}{9.12}+\frac{3}{12.15}+...+\frac{3}{270.273}\right)\)
\(A=\frac{4}{3}\left(\frac{12-9}{9.12}+\frac{15-12}{12.15}+...+\frac{273-270}{270.273}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{9}-\frac{1}{12}+\frac{1}{12}-\frac{1}{15}+...+\frac{1}{270}-\frac{1}{273}\right)\)
\(A=\frac{4}{3}\left(\frac{1}{9}-\frac{1}{273}\right)\)
\(A=\frac{352}{2457}\)