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Answers ( 3 )
  • See question detail

    We have :

    \(\dfrac{1}{3}+\dfrac{1}{31}+\dfrac{1}{35}+\dfrac{1}{37}+\dfrac{1}{47}+\dfrac{1}{53}+\dfrac{1}{61}\)

    \(=\dfrac{1}{3}+\left(\dfrac{1}{31}+\dfrac{1}{35}+\dfrac{1}{37}\right)+\left(\dfrac{1}{47}+\dfrac{1}{53}+\dfrac{1}{61}\right)\)

    \(< \dfrac{1}{3}+\left(\dfrac{1}{30}+\dfrac{1}{30}+\dfrac{1}{30}\right)+\left(\dfrac{1}{45}+\dfrac{1}{45}+\dfrac{1}{45}\right)\)

    \(=\dfrac{1}{3}+\dfrac{1}{10}+\dfrac{1}{15}=\dfrac{1}{2}\)

    => \(\dfrac{1}{3}+\dfrac{1}{31}+\dfrac{1}{35}+\dfrac{1}{37}+\dfrac{1}{47}+\dfrac{1}{53}+\dfrac{1}{61}< \dfrac{1}{2}\)

  • See question detail

    There are three ways to choose hundred of digits 

    There are three dozen digit selectors

    There are two ways to select the unit - number 

    It is possible to write three digit whole number 

    3 x 3 x 2 = 18 ( number )

  • See question detail

    The rectangular or trapezoidal length is large 

    60 : 5 = 12 ( cm )

    That trapezoidal baby is :

    12 - 2 - 2 = 8 ( cm )

    Trapezoidal area MNCD is 

    \(\dfrac{\left(8+12\right)\times5}{2}=50\)( cm2 )

    This is the 1st level solution 

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