CMR 1/26+1/27+1/28+…+1/50=1-1/2+1/3-1/4+…+1/49-1/50

CMR 1/26+1/27+1/28+…+1/50=1-1/2+1/3-1/4+…+1/49-1/50

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  1. Đáp án:

     

    Giải thích các bước giải:

    1/26+1/27+1/28+….+1/50=1-1/2+1/3-1/4+……+1/49-1/50=1-1/2+1/3-1/4+…+1/49-1/50

    =(1+1/3+1/5+…+1/49)-(1/2+1/4+…+1/50)

    =(1+1/2+1/3+….+1/50)-2.(1/2+1/4+…+1/50)

    =(1+1/2+1/3+…+1/50)-(1+1/2+1/3+…+1/25)

    =1/26+1/27+…..+1/50

    =0,020…

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  2. 1/26+1/27+1/28+….+1/50=1-1/2+1/3-1/4+……+1/49-1/50

    =1-1/2+1/3-1/4+…+1/49-1/50=(1+1/3+1/5+…+1/49)-(1/2+1/4+…+1/50)

    =(1+1/2+1/3+….+1/50)-2.(1/2+1/4+…+1/50)

    =(1+1/2+1/3+…+1/50)-(1+1/2+1/3+…+1/25)

    =1/26+1/27+…..+1/50

    ⇒ ĐPCM

     

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