chứng minh 1/2! + 2/3! + 3/4! +…..+99/100! <1

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chứng minh 1/2! + 2/3! + 3/4! +…..+99/100! <1

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Farah 1 year 2020-11-27T03:05:52+00:00 1 Answers 41 views 0

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    2020-11-27T03:07:01+00:00

    Giải thích các bước giải:

    $C= \dfrac{1}{2!}+\dfrac{2}{3!}+\dfrac{3}{4!}+…+\dfrac{99}{100!}$
     $= \dfrac{2-1}{2!}+\dfrac{3-1}{3!}+…+\dfrac{100-1}{100!}$
     $= \dfrac{2}{2!}-\dfrac{1}{2!}+\dfrac{3}{3!}-\dfrac{1}{3!}+…+\dfrac{100}{100!}-\dfrac{1}{100!}$
     $= \dfrac{1}{1!}-\dfrac{1}{2!}+\dfrac{1}{2!}-\dfrac{1}{3!}+\dfrac{1}{3!}-\dfrac{1}{4!}+…+\dfrac{1}{99!}-\dfrac{1}{100!}$
     $= 1-\dfrac{1}{100!}< 1$

     

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