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a: \(=\left(4+\dfrac{3}{4}+\dfrac{1}{8}+3+\dfrac{1}{12}\right)+\left(-0.37-1.28-2.5\right)=\dfrac{191}{24}-\dfrac{83}{20}=\dfrac{457}{120}\)
b: \(=\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{59}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}\cdot\dfrac{56}{305}=\dfrac{84}{305}\)
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=1/2*2/9+1/2*3/7-1/2*5/27
=1/9-5/54+3/14
=1/54+3/14
=44/189
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d: =>x+1/2=0 hoặc 2/3-2x=0
=>x=-1/2 hoặc x=1/3
b: \(\Leftrightarrow1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+...+\dfrac{1}{5x+1}-\dfrac{1}{5x+6}=\dfrac{2010}{2011}\)
\(\Leftrightarrow1-\dfrac{1}{5x+6}=\dfrac{2010}{2011}\)
=>1/(5x+6)=1/2011
=>5x+6=2011
=>5x=2005
hay x=401
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S=1/5^2+1/7^2+...+1/103^2
=>\(S< \dfrac{1}{5^2}+\dfrac{1}{5\cdot7}+\dfrac{1}{7\cdot9}+...+\dfrac{1}{101\cdot103}\)
=>\(S< \dfrac{1}{2\cdot5}+\dfrac{1}{2}\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{101}-\dfrac{1}{103}\right)\)
=>S<1/25+49/515<5/32
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(x - 1)² = 16
x - 1 = 4 hoặc x - 1 = -4
*) x - 1 = 4
x = 4 + 1
x = 5 (nhận)
*) x - 1 = -4
x = -4 + 1
x = -3 (loại
Vậy x = 5
(x-1)2 = 16
(x-1)2 = 42
x - 1 = 4
x = 4 + 1
x = 5
Vậy x = 5.
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\(\left|2x-9\right|=13\)
\(\Rightarrow\orbr{\begin{cases}2x-9=13\\2x-9=-13\end{cases}\Rightarrow\orbr{\begin{cases}2x=22\\2x=-4\end{cases}\Rightarrow}\orbr{\begin{cases}x=11\\x=-2\end{cases}}}\)
Vậy x = 11, x = -2
Vì |2x-9|=13 nên:
TH1:2x-9=13 TH2:2x-9=-13
2x=22 2x=-4
x=11 x=-2
Vậy x thuộc 11 và -2.
Chúc em học tốt^^
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