Tính tích P = 1 - 1 2 . 1 - 1 3 . 1 - 1 4 . . . . . 1 - 1 99
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{98}{99}\)
\(=\frac{1}{99}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(P=\left[1-\frac{1}{2}\right]\left[1-\frac{1}{3}\right]\left[1-\frac{1}{4}\right]...\left[1-\frac{1}{99}\right]\)
\(=\left[\frac{2}{2}-\frac{1}{2}\right]\left[\frac{3}{3}-\frac{1}{3}\right]\left[\frac{4}{4}-\frac{1}{4}\right]...\left[\frac{99}{99}-\frac{1}{99}\right]\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{98}{99}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot98}{2\cdot3\cdot4\cdot...\cdot99}=\frac{1}{99}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(P=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right)\)
\(P=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{98}{99}\)
\(P=\frac{1.2.3...98}{2.3.4...99}=\frac{1}{99}\)
Ta có: \(P=\left\{1-\frac{1}{2}\right\}.\left\{1-\frac{1}{3}\right\}....\left\{1-\frac{1}{99}\right\}\)
\(\Rightarrow P=\frac{1}{2}.\frac{2}{3}.........\frac{98}{99}\)\(=\frac{1.2.3...98}{2.3.4...99}=\frac{1}{99}\)
Vậy \(P=\frac{1}{99}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(P=\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).................\left(1-\frac{1}{999}\right).\left(1-\frac{1}{1000}\right)\)
\(P=\frac{-1}{2}.\frac{-2}{3}.......................\frac{-998}{999}.\frac{-999}{1000}\)
\(P=\frac{\left(-1\right).\left(-2\right)...............\left(-998\right).\left(-999\right)}{2.3........................999.1000}\)
\(P=\frac{-1}{1000}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{999}\right).\left(1-\frac{1}{1000}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{998}{999}.\frac{999}{1000}\)
\(=\frac{1.2.3.....998.999}{2.3.4.....999.1000}\)
\(=\frac{1}{1000}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
P=(1-1/2)(1-1/3)(1-1/4)....(1-1/100)
P=1/2.2/3.3/4.......99/100
P=(1.2.3....99)/(2.3.4...100)=1/100
Vậy P=1/100