Câu hỏi cần trả lờihehsjshsjjshsbsbsbshshshshhshs

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Câu hỏi cần trả lờihehsjshsjjshsbsbsbshshshshhshs
cau-hoi-can-tra-loihehsjshsjjshsbsbsbshshshshhshs

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Lệ Thu 5 years 2021-05-23T19:51:38+00:00 1 Answers 23 views 0

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  1. Nho
    0
    2021-05-23T19:53:18+00:00
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    Giải thích các bước giải:

     B4:

    a) Ta có:

    $\begin{array}{l}
    S = \dfrac{2}{{3.5}} + \dfrac{3}{{5.8}} + \dfrac{4}{{8.12}} + … + \dfrac{{14}}{{93.107}} + \dfrac{{15}}{{107.122}} + \dfrac{{16}}{{122.138}}\\
     = \dfrac{{5 – 3}}{{3.5}} + \dfrac{{8 – 5}}{{5.8}} + \dfrac{{12 – 8}}{{8.12}} + … + \dfrac{{107 – 93}}{{93.107}} + \dfrac{{122 – 107}}{{107.122}} + \dfrac{{138 – 122}}{{122.138}}\\
     = \left( {\dfrac{1}{3} – \dfrac{1}{5}} \right) + \left( {\dfrac{1}{5} – \dfrac{1}{8}} \right) + \left( {\dfrac{1}{8} – \dfrac{1}{{12}}} \right) + … + \left( {\dfrac{1}{{93}} – \dfrac{1}{{107}}} \right) + \left( {\dfrac{1}{{107}} – \dfrac{1}{{122}}} \right) + \left( {\dfrac{1}{{122}} – \dfrac{1}{{138}}} \right)\\
     = \dfrac{1}{3} – \dfrac{1}{{138}}\\
     = \dfrac{{46 – 1}}{{138}}\\
     = \dfrac{{45}}{{138}}\\
     = \dfrac{{15}}{{46}}
    \end{array}$

    Vậy $S = \dfrac{{15}}{{46}}$

    b) Ta có:

    $\begin{array}{l}
    A = \dfrac{n}{{n + 1}} + \dfrac{{n + 3}}{{n + 1}}\\
     = \dfrac{{2n + 3}}{{n + 1}}\\
     = \dfrac{{2\left( {n + 1} \right) + 1}}{{n + 1}}\\
     = 2 + \dfrac{1}{{n + 1}}
    \end{array}$

    Để $A \in Z$

    $\begin{array}{l}
     \Leftrightarrow 2 + \dfrac{1}{{n + 1}} \in Z\\
     \Leftrightarrow \dfrac{1}{{n + 1}} \in Z\\
     \Leftrightarrow n + 1 \in U\left( 1 \right) = \left\{ { – 1;1} \right\}\left( {do:n + 1 \in Z} \right)\\
     \Leftrightarrow n \in \left\{ { – 2;0} \right\}
    \end{array}$

    Vậy $n \in \left\{ { – 2;0} \right\}$ thỏa mãn đề.

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