\(B=\frac{10}{18}\times\frac{22}{30}\times\frac{36}{44}\times...\times\frac{200}{209}=\frac{1\times10}{2\times9}\times\frac{2\times11}{3\times10}\times\frac{3\times12}{4\times11}\times...\times\frac{10\times20}{11\times19}\)
\(=\frac{1\times10\times2\times11\times3\times12\times...\times10\times20}{2\times9\times3\times10\times4\times11\times...\times11\times19}=\frac{\left(1\times2\times3\times...\times10\right)\times\left(10\times11\times12\times...\times20\right)}{\left(2\times3\times4\times...\times11\right)\times\left(9\times10\times11\times...\times19\right)}\)
\(=\frac{1\times20}{11\times9}=\frac{20}{99}\)
Sửa đề \(C=\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{16}\right)\times...\times\left(1-\frac{1}{100}\right)\)
\(=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...\times\frac{99}{100}=\frac{3\times8\times15\times...\times99}{4\times9\times16\times...\times100}=\frac{1\times3\times2\times4\times3\times5\times...\times9\times11}{2\times2\times3\times3\times4\times4\times...\times10\times10}\)
\(=\frac{\left(1\times2\times3\times....\times9\right)\times\left(3\times4\times5\times...\times11\right)}{\left(2\times3\times4\times...\times10\right)\times\left(2\times3\times4\times...\times10\right)}=\frac{1\times11}{10\times2}=\frac{11}{20}\)
b) C=(1- 1/4) x (1- 1/9) x (1-1/16) x (1- 1/100)
C = 3/4 . 8/9 . 15/16.......99/100
C= 3.8.15....99/4.9.16...100
C= 1.3.2.4.3.5....9.11/ 2.2.3.3.4.4......10.10
C= 1.2.3.4...9/ 2.3.4.5....10 . 3.4.5....11/ 2.3.4.5...10
C= 1/10 . 11/2
C= 11/20
Mk nghĩ đề nt mới đúng
Câu a) để sau
b)\(C=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)\left(1-\frac{1}{100}\right)\)
\(C=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{99}{100}\)
\(C=\frac{3\cdot8\cdot15\cdot99}{4\cdot9\cdot16\cdot100}\)
\(C=\frac{3\cdot4\cdot2\cdot3\cdot5\cdot11\cdot9}{2\cdot2\cdot3\cdot3\cdot4\cdot4\cdot5\cdot20}=\frac{11\cdot9}{2\cdot4\cdot20}=\frac{99}{160}\)
11/20 bạn ạ mk giải ra nhưng ko muốn nhăn dài
