Giải giúp mình ạ mình cảm ơn

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Giải giúp mình ạ mình cảm ơn
giai-giup-minh-a-minh-cam-on

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Thanh Hà 9 months 2021-05-14T04:43:26+00:00 1 Answers 1 views 0

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    2021-05-14T04:44:56+00:00

    $\begin{array}{l}a)\ A=53.81-47.14+81.47-14.53\\\to A=81.(53+47)-14.(47+53)\\\to A=(81-14)(47+53)\\\to A=67.100\\\to A=6700\\\,\\b)\ B=\left|1-2^{100}\right|+\left|5^{50}-2^{100}\right| -\left|11-5^{50}\right|\\\text{- Ta có : $1<2^{100}$ (hiển nhiên)}\\\to 1-2^{100}<0\\\to\left|1-2^{100}\right|=-\left(1-2^{100}\right)=-1+2^{100}\\\quad 5^{50}>4^{50}=2^{100}\\\to 5^{50}>2^{100}\\\to5^{50}-2^{100}>0\\\to\left|5^{50}-2^{20}\right|=5^{50}-2^{100}\\\quad11<5^{50}\ \rm(hiển\ nhiên)\\\to11-5^{50}<0\\\to \left|11-5^{50}\right|=-\left(11-5^{50}\right)=-11+5^{50}\\\text{- Vậy $B=-1+2^{100}+5^{50}-2^{100}-\left(-11+5^{50}\right)$}\\\to B=-1+2^{100}+5^{50}-2^{100}+11-5^{50}\\\to B=(-1+11)+\left(2^{100}-2^{100}\right)+\left(5^{50}-5^{50}\right)\\\to B=10\\\,\\c)\ C=\dfrac2{1.4}+\dfrac2{4.7}+\dfrac2{7.10}+\ldots+\dfrac2{97.100}\\\to C=\dfrac23\left(\dfrac3{1.4}+\dfrac3{4.7}+\dfrac3{7.10}+\ldots+\dfrac3{97.100}\right)\\\to C=\dfrac23\left(1-\dfrac14+\dfrac14-\dfrac17+\ldots+\dfrac1{97}-\dfrac1{100}\right)\\\to C=\dfrac23\left(1-\dfrac1{100}\right)\\\to C=\dfrac23\cdot\dfrac{99}{100}\\\to C=\dfrac{33}{50}\\\,\\d)\ D=\left(1+\dfrac1{1.3}\right)\left(1+\dfrac1{2.4}\right)\left(1+\dfrac1{3.5}\right)\ldots\left(1+\dfrac1{2019.2021}\right)\\\to D=\dfrac{4}{1.3}\cdot\dfrac{9}{2.4}\cdot\dfrac{16}{3.5}\ldots\dfrac{4080400}{2019.2021}\\\to D=\dfrac{2.2}{1.3}\cdot\dfrac{3.3}{2.4}\cdot\dfrac{4.4}{3.5}\ldots\dfrac{2020.2020}{2019.2021}\\\to D=\dfrac{2.2.3.3.4.4\dots2020.2020}{1.3.2.4.3.5\dots2019.2021}\\\to D=\dfrac{(2.3.4\dots2020)(2.3.4\dots2020)}{(1.2.3.4\dots2019)(3.4.5.6\dots2020.2021)}\\\to D=\dfrac{2.3.4\dots2020}{1.2.3\dots2019}\cdot\dfrac{2.3.4.5\dots2020}{3.4.5\dots2021}\\\to D=2020\cdot\dfrac2{2021}\\\to D=\dfrac{4040}{2021} \end{array}$

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