Tính K=(1-3/8)x(1-3/15)x(1-3/24)...x(1-3/399)
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a) 2/3 : 3/5 × 5/7 : 2/3
= 2/3 × 5/3 × 5/7 × 3/2
= 25/21
b) 1 1/2 × 1 1/3 × 1 1/18 × 1 1/15 × 1 1/24 × 1 1/35
= 3/2 × 4/3 × 19/18 × 16/15 × 25/24 × 36/35
= 2 × 152/35 × 15/14
= 304/35 × 15/14
= 152/7
\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot\dfrac{16}{15}\cdot\dfrac{25}{24}\cdot\dfrac{36}{35}=\dfrac{12}{7}\)
= 4/3*9/8*16/15*25/24*36/35
=2*2/1*3 * 3*3/2*4 *4*4/3*5 *5*5/4*6 * 6*6/5*7
= (2*3*4*5*6 / 1*2*3*4*5) * ( 2*3*4*5*6 / 3*4*5*6*7)
=6/1* 2/7
= 12/7
ban lam sai rui de mk lam lai nhe.
\(12.\left(x-1\right):3=4^3-2^3\)
\(12.\left(x-1\right):3=64-8\)
\(12.\left(x-1\right):3=56\)
\(12.\left(x-1\right)=56.3\)
\(12.\left(x-1\right)=168\)
\(x-1=168:12\)
\(x-1=14\)
\(x=15\)
1/3x1/8x...x1/99
=1/(1x3)x1/(2x4)x...x1/(9x11)
=1/(1x3x2x4x...x9x11)
=1/(1x2x3x3x4x4x5x5x...x9x9x10x11)
\(K=\left(1-\dfrac{3}{2\cdot4}\right)\left(1-\dfrac{3}{3\cdot5}\right)\cdot...\cdot\left(1-\dfrac{3}{19\cdot21}\right)\)
\(=\dfrac{3^2-1-3}{\left(3-1\right)\left(3+1\right)}\cdot\dfrac{4^2-1-3}{\left(4-1\right)\left(4+1\right)}\cdot...\cdot\dfrac{20^2-4}{\left(20-1\right)\left(20+1\right)}\)
\(=\dfrac{\left(3-2\right)\left(3+2\right)}{\left(3-1\right)\left(3+1\right)}\cdot\dfrac{\left(4-2\right)\left(4+2\right)}{\left(4-1\right)\left(4+1\right)}\cdot...\cdot\dfrac{18\cdot22}{\left(20-1\right)\left(20+1\right)}\)
\(=\dfrac{1\cdot5}{2\cdot4}\cdot\dfrac{2\cdot6}{3\cdot5}\cdot...\cdot\dfrac{18\cdot22}{19\cdot21}\)
\(=\dfrac{1\cdot2\cdot3\cdot...\cdot21\cdot22}{2\cdot3\cdot4\cdot5\cdot...\cdot19\cdot20\cdot21}=1\cdot22=22\)