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\(S=\dfrac{1}{5\cdot9}+\dfrac{1}{9\cdot13}+\dfrac{1}{13\cdot17}+....+\dfrac{1}{41\cdot45}\)
\(S=\dfrac{1}{4}\cdot\left(\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+\dfrac{4}{13\cdot17}+....+\dfrac{4}{41\cdot45}\right)\)
\(S=\dfrac{1}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{17}+....+\dfrac{1}{41}-\dfrac{1}{45}\right)\)
\(S=\dfrac{1}{4}\cdot\left(\dfrac{1}{5}-\dfrac{1}{45}\right)\)
\(S=\dfrac{1}{4}\cdot\dfrac{8}{45}=\dfrac{2}{45}\)
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1)
25 x 7 + 3 x (50-25) x (60 - 60)
=175 +3 x 25 x 0
=175
2)
\(\frac{1}{2}.\frac{3}{4}.\frac{4}{5}.\frac{1}{3}\\ =\frac{1.3.4.1}{2.4.5.3}\\ =\frac{3.4}{3.4.2.5}\\ =\frac{1}{2.5}\\ =\frac{1}{10}\)
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\(\left(\dfrac{2+1}{2}\right)\left(\dfrac{3+1}{3}\right)\left(\dfrac{4+1}{4}\right)...\left(\dfrac{2000+1}{2000}\right)\)
\(=\dfrac{3.4.5...2001}{2.3.4...2000}=\dfrac{2001}{2}\)
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Ta có:A=(1−12)×(1−13)×.......×(1−12000)A=(1−12)×(1−13)×.......×(1−12000)
=12×23×34×..........×19992000=12×23×34×..........×19992000
=12000=12000
Vậy giá trị của A là:12000
\(=\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{2001}{2000}=\dfrac{2001}{2}\)
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27/28 = 3x9 / (4x7) = 3/4 x 9/7 27/28 x 35/36 = (3x9) / (4x7) x (5x7) / (4x9) = 3/4 x 5/4 27/28 x 35/36 x 44/45 = 3x5/(4x4) x 4x11/5x9 = 3/4 x 11/9 ...... xxxxxx .... x (49x101)/(50x99) = 3/4 x 101/99
23,433+3792833+3647,2 X 222222222267,1= 8,10488893e14