So sánh A=1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20 và 7/12

0 bình luận về “So sánh A=1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20 và 7/12”

1. Ta có: `1/11>1/20; 1/12>1/20; 1/13>1/20;…;1/19>1/20`

   `=> 1/11+1/12+1/13+…+1/20>1/20+1/20+…+1/20`(`10` số hạng)

   `=> 1/11+1/12+..+1/20>10/20`

   `=> A>1/2`

    

   Trả lời

2. Đáp án:

   `A>7/12`

   Giải thích các bước giải:

   Ta có `1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20`

   `=(1/11+1/12+1/13+1/14+1/15)+(1/16+1/17+1/18+1/19+1/20)`

   Ta thấy `1/11>1/15;1/12>1/15;1/13>1/15;1/14>1/15`

   `=>1/11+1/12+1/13+1/14+1/15>1/15+1/15+1/15+1/15+1/15` (Có `5` số hạng)

   `=>1/11+1/12+1/13+1/14+1/15>1/3` `(1)`

   Ta thấy `1/16>1/20;1/17>1/20;1/18>1/20;1/19>1/20`

   `=>1/16+1/17+1/18+1/19+1/20>1/20+1/20+1/20+1/20` (Có `5` số hạng)

   `=>1/16+1/17+1/18+1/19+1/20>1/4` `(1)`

   Từ `(1)` và `(2)` ta có:

   `1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20>1/3+1/4=7/12`

   Vậy `1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20>7/12`.

   Trả lời