chứng minh: 1/4+1/16+1/36+…+1/10000<1/2

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chứng minh: 1/4+1/16+1/36+…+1/10000<1/2

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Serenity 1 tháng 2021-08-05T16:39:43+00:00 2 Answers 4 views 0

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    2021-08-05T16:41:29+00:00

    đây

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    2021-08-05T16:41:41+00:00

    Đặt `A= 1/4 + 1/16 + 1/36 +…+ 1/10000`

    `A= 1/4 ( 1 + 1/4 + 1/9 + …+ 1/2500)`

    `A= 1/4 ( 1 + 1/2.2 + 1/3.3 +…+ 1/50.50)`

    `A < 1/4 ( 1 + 1/1.2 + 1/2.3 +…+ 1/49.50)`

    `A< 1/4( 1+ 1/1 – 1/2 + 1/2 -1/3 +… + 1/49 – 1/50)`

    `A< 1/4 ( 1 + 1 – 1/50)`

    `A< 1/4 ( 2 – 1/50)`

    `A< 1/2 – 1/200 < 1/2`

    Vậy `A< 1/2`

     

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