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Đặt \(A=\frac{3\cdot7\cdot13\cdot37\cdot39-10101}{505050-70707}\)
\(A=\frac{\left(3\cdot7\cdot13\cdot37\right)\cdot39-10101\cdot1}{50\cdot10101+7\cdot10101}\)
\(A=\frac{10101\cdot39-10101\cdot1}{10101\cdot\left(50+7\right)}\)
\(A=\frac{10101\cdot\left(39-1\right)}{10101\cdot57}\)
\(A=\frac{10101\cdot38}{10101\cdot57}\)
\(A=\frac{38}{57}=\frac{38:19}{57:19}=\frac{2}{3}\)
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a) 544544 – 444444 = 544.1001 – 444.1001 = 1001.(544 – 444) = 1001.100 = 100100
b) 131313 – 10101 – 20202 = 10101.13 – 10101 – 10101.2
= 10101.(13 – 1 – 2) = 10101.10 = 101010
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\(A=\dfrac{1}{2020}+\dfrac{1}{2020^2}+...+\dfrac{1}{2020^{2021}}\)
\(\Rightarrow2020A=1+\dfrac{1}{2020}+...+\dfrac{1}{2020^{2020}}\)
\(\Rightarrow2020A-A=\left(1+\dfrac{1}{2020}+...+\dfrac{1}{2020^{2020}}\right)-\left(\dfrac{1}{2020}+\dfrac{1}{2020^2}+...+\dfrac{1}{2020^{2021}}\right)\)
\(\Rightarrow2019A=1-\dfrac{1}{2020^{2021}}< 1\Rightarrow A< \dfrac{1}{2019}\)
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\(\dfrac{121212}{353535}+-\dfrac{2323}{4242}\)
\(=\dfrac{12}{35}+-\dfrac{23}{42}\)
\(=-\dfrac{43}{210}\)
\(=\dfrac{12}{35}-\dfrac{23}{42}=\dfrac{72-115}{210}=\dfrac{-43}{210}\)
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so sánh hả bạn?
ta có : 191919 + 20202 = 212121
353535 + 70707 = 424242
vì 212121 < 424242
=> 191919 + 20202 < 353535 + 70707