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![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).......\left(1-\frac{1}{2004}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}....\frac{2003}{2004}\)
\(=\frac{1}{2004}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\frac{3}{2}\cdot\frac{4}{3}\cdot.....\cdot\frac{2014}{2013}\)
\(=\frac{2}{2013}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(B=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)........\left(1-\frac{1}{2017}\right).\left(1-\frac{1}{2018}\right)\)
\(\Rightarrow B=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.......\frac{2016}{2017}.\frac{2017}{2018}\)
Đởn giản hết sẽ còn là:
\(\Rightarrow B=\frac{1}{2018}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x...x\frac{2006}{2007}=\frac{1}{2007}\)
k nha bạn
![](https://rs.olm.vn/images/avt/0.png?1311)
Vì \(\orbr{\begin{cases}\left|2x-6\right|\ge0\forall x\\\left|3y+9\right|\ge0\forall y\end{cases}}\Rightarrow-\left|2x-6\right|-\left|3y+9\right|\le0\forall x;y\)
\(\Rightarrow-18-\left|2x-6\right|-\left|3y+9\right|\le-18\)
Dấu "=" xảy ra \(\Leftrightarrow\orbr{\begin{cases}\left|2x-6\right|=0\\\left|3y+9\right|=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\y=-3\end{cases}}\)
Vậy maxC = - 18 <=> x = 3 ; y = - 3
Lớp 5 đã học rồi cơ à :)) Giỏi thế
C = -18 - | 2x - 6 | - | 3y + 9 |
Ta có : \(\hept{\begin{cases}-\left|2x-6\right|\le0\forall x\\-\left|3y+9\right|\le0\forall y\end{cases}}\Rightarrow-18-\left|2x-6\right|-\left|3y+9\right|\le-18\forall x,y\)
Đẳng thức xảy ra <=> \(\hept{\begin{cases}2x-6=0\\3y+9=0\end{cases}}\Rightarrow\hept{\begin{cases}x=3\\y=-3\end{cases}}\)
=> MaxC = -18 <=> x = 3, y = -3
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right).\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{98}{99}.\frac{99}{100}\) \(=\frac{1.2.3...98.99}{2.3.4...99.100}=\frac{1}{100}\)
nha