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\(=3^2\cdot\dfrac{1}{6}\left(\dfrac{6}{10\cdot16}+\dfrac{6}{16\cdot22}+...+\dfrac{6}{100\cdot106}\right)\)
\(=\dfrac{3}{2}\left(\dfrac{1}{10}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{22}+...+\dfrac{1}{100}-\dfrac{1}{106}\right)\)
\(=\dfrac{3}{2}\cdot\left(\dfrac{1}{10}-\dfrac{1}{106}\right)\)
\(=\dfrac{3}{2}\cdot\dfrac{24}{265}=\dfrac{36}{265}\)
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Đặt \(A=\dfrac{1}{1.2}+\dfrac{2}{2.4}+\dfrac{3}{4.7}+\dfrac{4}{7.11}+\dfrac{5}{11.16}+\dfrac{6}{16.22}\)
\(1A=1-\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(\dfrac{1}{4}+\dfrac{1}{4}\right)+\left(\dfrac{1}{7}+\dfrac{1}{7}\right)+\left(\dfrac{1}{11}+\dfrac{1}{11}\right)+\left(\dfrac{1}{16}+\dfrac{1}{16}\right)-\dfrac{1}{22}\)\(1A=1-\dfrac{1}{22}\)
\(1A=\dfrac{22}{22}-\dfrac{1}{22}\)
\(1A=\dfrac{21}{22}\)
\(\dfrac{21}{22}\) không thể rút gọn
\(A=\dfrac{1}{1\cdot2}+\dfrac{2}{2\cdot4}+\dfrac{3}{4\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{5}{11\cdot16}+\dfrac{6}{16\cdot22}\\ =\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{22}\\ =1-\dfrac{1}{22}\\ =\dfrac{21}{22}\)
Vậy \(A=\dfrac{21}{22}\)
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\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{22}+\dfrac{1}{22}-\dfrac{1}{29}\)
=1-1/29
=28/29
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1
= 25 * ( - 21 ) + 25 * 72 + 49 * 25
= 25 * ( -21 + 72 + 49 )
= 25 * 100 = 2500
2
= 16 * 2 * (-39) + 16 * 2*11
= 16 * 2 * (-39+ 11)
= 32 * (-28) = (-896)
3
= 22 * 2 * ( - 36 ) + 22 * ( - 28 )
= 22 * {( 2 * [( - 36 ) + ( - 28 )]}
= 22 * ( - 100 )
= ( -2200 )
4
=> x - 2 = 3 hoặc ( - 3 )
Nếu x - 2 = 3
=> x = 5
Nếu x - 2 = ( - 3 )
=> x = -1
Vậy x = 5 hoặc x = -1
5
=> |x - 3 | = 13 + 7
=> |x - 3 | = 20
=> x - 3 = 20 hoặc ( -20 )
Nếu x - 3 = 20
=> x = 23
Nếu x - 3 = ( - 20 )
=> x = -17
Vậy x = 23 hoặc x = - 17
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\(3\cdot5^2-16\cdot2^2\)
\(=3\cdot25-16:4\)
\(=75-4\)
\(=71\)
==============
\(2^3\cdot17-2^3\cdot14\)
\(=2^3\cdot\left(17-14\right)\)
\(=2^3\cdot3\)
\(=8\cdot3\)
\(=24\)
===============
\(15\cdot141+59\cdot15\)
\(=15\cdot\left(141+59\right)\)
\(=15\cdot200\)
\(=3000\)
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\(17\cdot85+15\cdot17-120\)
\(=17\cdot\left(85+15\right)-120\)
\(=17\cdot100-120\)
\(=1700-120\)
\(=1580\)
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\(20-\left[30-\left(5-1\right)^2\right]\)
\(=20-\left(30-4^2\right)\)
\(=20-\left(30-16\right)\)
\(=20-14\)
\(=6\)
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