S=1/31+1/32+1/33+………..+1/60 chứng minh S<4/5

Question

S=1/31+1/32+1/33+………..+1/60 chứng minh S<4/5

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Gabriella 2 tháng 2021-10-12T08:02:01+00:00 2 Answers 7 views 0

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    0
    2021-10-12T08:03:28+00:00

    S=[$\frac{1}{31}$+$\frac{1}{32}$+…+$\frac{1}{40}$]+[$\frac{1}{41}$+$\frac{1}{42}$+…+$\frac{1}{50}$]+[$\frac{1}{51}$+$\frac{1}{52}$+…+$\frac{1}{60}$]

    Mà:$\frac{1}{31}$+$\frac{1}{32}$+…+$\frac{1}{40}$<$\frac{1}{31}$×10=$\frac{10}{31}$

    Vì $\frac{10}{31}$<$\frac{4}{5}$

    ⇔S<$\frac{4}{5}$

    0
    2021-10-12T08:03:55+00:00

    Giải thích các bước giải:

    1/31 > 1/60; 1/32 > 1/60; 1/33 > 1/60; …; 1/59 > 1/60

    => (1/31 + 1/32 + 1/33 + … + 1/60) > (1/60 + 1/60 + 1/60 + … + 1/60)

    => (1/31 + 1/32 + 1/33 + … + 1/60) > 30/60

    => (1/31 + 1/32 + 1/33 + … + 1/60) > 1/2

    => S > 1/2

    Vì 4/5 > 1/2 nên 4/5 > S => S < 4/5 (đccm)

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