1) Tính A = ( 1 – 1/2 ) . ( 1 – 1/3) . ( 1 – 1/4) 2) Chứng tỏ a) B = 1/2 mũ 2 + 1/3 mũ 2 + 1/4 mũ 2 + …+ 1/201- mũ 2 < 1 b) C = 3/2.5 + 3/5.8 + 3/8.

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1. Đáp án:

    

   Giải thích các bước giải:

    `1)A=(1 -1/2).(1 -1/3).(1-1/4)`

   `A=1/2 . 2/3 .3/4`

   `A=1/4`

   `2)`

   `a)B=1/2^2 +1/3^2+1/4^2+…+1/201^2`

   `B=1/2.2 +1/3.3 +1/4.4 +…+1/201.201`

   `B<1/1.2 +1/2.3 +1/3.4 +…+1/200.201`

   `A<1 -1/2+1/2-1/3+1/3-1/4+…+1/200-1/201`

   `A<1-1/201<1`

   `=>A<1`

   `b)C = 3/2.5 + 3/5.8 + 3/8.11 + 3/11.14 + 3/14.17`

   `C=1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17`

   `C=1/2-1/17<1/2`

   `=>C<1/2`

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