Tính tổng S=1/1.3+1/3.5+1/5.7+…+1/99.101

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Tính tổng
S=1/1.3+1/3.5+1/5.7+…+1/99.101

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Emery 2 tháng 2021-10-01T11:38:54+00:00 2 Answers 8 views 0

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    0
    2021-10-01T11:40:24+00:00

    S=1/1.3+1/3.5+1/5.7+…+1/99.101

    2S= 2/1.3+2/3.5+2./5.7+…+2/99.101

    = 1-1/3+1/3-1/5+1/5-1/7+…+1/99-1/101

    = 1-1/101

    = 100/101

    => S= 100/101: 2 = 50/101

    0
    2021-10-01T11:40:34+00:00

    Đáp án:

    $\dfrac{50}{101}$

    Giải thích các bước giải:

    \(\begin{array}{l}S = \dfrac{1}{1.3} + \dfrac{1}{3.5} + \dfrac{1}{5.7} + … + \dfrac{1}{99.1011}\\S = \dfrac{1}{{1.3}} + \dfrac{1}{{3.5}} + \dfrac{1}{{5.7}} + … + \dfrac{1}{{99.101}}\\ = \dfrac{1}{2}.\left( {1 – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{5} + \dfrac{1}{5} – \dfrac{1}{7} + … + \dfrac{1}{{99}} – \dfrac{1}{{101}}} \right)\\ = \dfrac{1}{2}.\left( {1 – \dfrac{1}{{101}}} \right)\\ = \frac{1}{2}.\dfrac{{100}}{{101}}\\ = \dfrac{{50}}{{101}}\end{array}\)

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