Héo mi mọi người ơi Nhớ chuẩn đó 1/2+ 1/6+1/12+1/20+……+ 1/110 < 1

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Héo mi mọi người ơi
Nhớ chuẩn đó 1/2+ 1/6+1/12+1/20+……+ 1/110 < 1

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Charlie 4 tuần 2021-09-16T18:02:34+00:00 2 Answers 2 views 0

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    0
    2021-09-16T18:03:34+00:00

    Đáp án:

    Ta có: $\frac{1}{2}$ + $\frac{1}{6}$ + $\frac{1}{20}$ + … + $\frac{1}{110}$ = $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + … + $\frac{1}{10.11}$ = 1 – $\frac{1}{2}$ + $\frac{1}{2}$ – $\frac{1}{3}$ + … – $\frac{1}{11}$ = 1 – $\frac{1}{11}$ < 1 (đpcm)

    Chúc bn học tốt! 

    Giải thích các bước giải:

     

    0
    2021-09-16T18:03:58+00:00

    $\ \dfrac{1}{2} + \dfrac{1}{6} + \dfrac{1}{12} + \dfrac{1}{20} + … + \dfrac{1}{110}$

    $\ = \dfrac{1}{1.2} + \dfrac{1}{2.3} + \dfrac{1}{3.4} + \dfrac{1}{4.5} + … + \dfrac{1}{10.11}$

    $\ = 1 – \dfrac{1}{2} + \dfrac{1}{2} – \dfrac{1}{3} + \dfrac{1}{3} – \dfrac{1}{4} + \dfrac{1}{4} – \dfrac{1}{5} + … + \dfrac{1}{10} – \dfrac{1}{11}$

    $\ = 1 – \dfrac{1}{11} = \dfrac{10}{11} < 1$ $\ (đpcm)$

    Vậy…

     

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