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Cho A= \(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+.......+\dfrac{1}{3^{2018}}+\dfrac{1}{3^{2019}}\) . Chứng minh rằng: A<\(\dfrac{1}{2}\)
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Tính
A ) (\(\dfrac{1}{3}\))2 . 9 . 3 -\(\dfrac{1}{2}\)
B) \(\dfrac{1}{4}\)+\(\dfrac{3}{4}\) . \(\dfrac{2}{5}\)
Tính:left(dfrac{9}{25}-2.18right):left(3dfrac{4}{5}+0,2right) dfrac{3}{8}.19dfrac{1}{3}dfrac{3}{8}.33dfrac{1}{3} 15.left(-dfrac{2}{3}right)^2-dfrac{7}{3} dfrac{1}{2}sqrt{64}-sqrt{dfrac{4}{25}}+left(-1right)^{2007} left(-dfrac{5}{2}right)^2:left(-15right)-left(0,45+dfrac{3}{4}right).left(-1dfrac{5}{9}right)left(dfrac{-1}{3}right)-left(dfrac{-3}{5}right)^0+left(1-dfrac{1}{2}right)^2:2 left(dfrac{1}{2}right)^{15}.left(dfrac{1}{4}right)^{20}dfrac{5^4.20}{25^5.4^5}
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Tính:
\(\left(\dfrac{9}{25}-2.18\right):\left(3\dfrac{4}{5}+0,2\right)\)
\(\dfrac{3}{8}.19\dfrac{1}{3}\dfrac{3}{8}.33\dfrac{1}{3}\)
\(15.\left(-\dfrac{2}{3}\right)^2-\dfrac{7}{3}\)
\(\dfrac{1}{2}\sqrt{64}-\sqrt{\dfrac{4}{25}}+\left(-1\right)^{2007}\)
\(\left(-\dfrac{5}{2}\right)^2:\left(-15\right)-\left(0,45+\dfrac{3}{4}\right).\left(-1\dfrac{5}{9}\right)\)
\(\left(\dfrac{-1}{3}\right)-\left(\dfrac{-3}{5}\right)^0+\left(1-\dfrac{1}{2}\right)^2:2\)
\(\left(\dfrac{1}{2}\right)^{15}.\left(\dfrac{1}{4}\right)^{20}\)
\(\dfrac{5^4.20}{25^5.4^5}\)
\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^24^2}+......+\dfrac{19}{9^2.10^2}\)
Chứng tỏ a <1
Cho A=1+\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2^{100}-1}\)
Chứng minh rằng 50<A<100
thực hiện phép tính (tính hợp lí nếu có thể)
1) left(-dfrac{1}{2}right)^2:dfrac{1}{4}-2.left(dfrac{-1}{2}right)^3+sqrt{4}
2) 3-left(dfrac{-6}{7}right)^0+sqrt{9}:2
3) left(-2right)^3+dfrac{1}{2}:dfrac{1}{8}-sqrt{25}+left|-64right|
4) left(-dfrac{1}{2}right)^4+left|-dfrac{2}{3}right|-2007^0
5) dfrac{left(0,4-dfrac{2}{9}+dfrac{2}{11}right)}{1,4-dfrac{7}{9}+dfrac{7}{11}}-dfrac{dfrac{1}{3}-0,25+dfrac{1}{5}}{1dfrac{1}{6}-0,875+0,7}
6) left[2^3.left(-dfrac{1}{2}right)^3+dfrac{1}{2}right]+left[dfr...
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thực hiện phép tính (tính hợp lí nếu có thể)
1) \(\left(-\dfrac{1}{2}\right)^2:\dfrac{1}{4}-2.\left(\dfrac{-1}{2}\right)^3+\sqrt{4}\)
2) \(3-\left(\dfrac{-6}{7}\right)^0+\sqrt{9}:2\)
3) \(\left(-2\right)^3+\dfrac{1}{2}:\dfrac{1}{8}-\sqrt{25}+\left|-64\right|\)
4) \(\left(-\dfrac{1}{2}\right)^4+\left|-\dfrac{2}{3}\right|-2007^0\)
5) \(\dfrac{\left(0,4-\dfrac{2}{9}+\dfrac{2}{11}\right)}{1,4-\dfrac{7}{9}+\dfrac{7}{11}}-\dfrac{\dfrac{1}{3}-0,25+\dfrac{1}{5}}{1\dfrac{1}{6}-0,875+0,7}\)
6) \(\left[2^3.\left(-\dfrac{1}{2}\right)^3+\dfrac{1}{2}\right]+\left[\dfrac{25}{22}+\dfrac{6}{25}-\dfrac{3}{22}+\dfrac{19}{25}+\dfrac{1}{2}\right]\)
tìm x biết
1) dfrac{2}{3}+dfrac{1}{3}:xdfrac{3}{5}
2) left(dfrac{2x}{3}-3right):left(-10right)dfrac{2}{5}
3) 2dfrac{2}{3}:x2dfrac{1}{12}:left(-0,06right)
4) dfrac{3}{7}+dfrac{1}{7}:xdfrac{3}{14}
5) -dfrac{3}{5}.x-dfrac{1}{2}-dfrac{1}{7}
6) dfrac{1}{5}+2x-2dfrac{1}{4}
7)-dfrac{1}{2}:xdfrac{3}{8}:dfrac{9}{16}
8)dfrac{2}{3}:x2dfrac{1}{2}:left(-0,3right)
9) dfrac{x}{3}dfrac{-2}{1,5}
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tìm x biết
1) \(\dfrac{2}{3}+\dfrac{1}{3}:x=\dfrac{3}{5}\)
2) \(\left(\dfrac{2x}{3}-3\right):\left(-10\right)=\dfrac{2}{5}\)
3) \(2\dfrac{2}{3}:x=2\dfrac{1}{12}:\left(-0,06\right)\)
4) \(\dfrac{3}{7}+\dfrac{1}{7}:x=\dfrac{3}{14}\)
5) \(-\dfrac{3}{5}.x-\dfrac{1}{2}=-\dfrac{1}{7}\)
6) \(\dfrac{1}{5}+2x=-2\dfrac{1}{4}\)
7)\(-\dfrac{1}{2}:x=\dfrac{3}{8}:\dfrac{9}{16}\)
8)\(\dfrac{2}{3}:x=2\dfrac{1}{2}:\left(-0,3\right)\)
9) \(\dfrac{x}{3}=\dfrac{-2}{1,5}\)
Cho \(A=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+...+\left(\dfrac{1}{2}\right)^{98}+\left(\dfrac{1}{2}\right)^{99}\)
Chứng minh : A<1
a, \(\dfrac{2}{3}-\dfrac{2}{5}+\dfrac{2}{9}+\dfrac{2}{13}\)/\(\dfrac{11}{3}-\dfrac{11}{5}+\dfrac{9}{11}+\dfrac{11}{3}\)