A=$\frac{1}{6}$ +$\frac{1}{7}$ + $\frac{1}{8}$ +…+$\frac{1}{20}$ Chứng Minh A>1

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1. Đáp án + Giải thích các bước giải:

   `A=1/6+1/7+1/8+….+1/20`

   `=(1/6+1/7+1/8+1/9+1/10)+(1/11+1/12+….+1/20)`

   `=B  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +C`

   $\\$

   `B=1/6+1/7+1/8+1/9+1/10`

   Có :

   `1/6>1/10`

   `1/7>1/10`

   `1/8>1/10`

   `1/9>1/10`

   `1/10=1/10`

   `to 1/6+1/7+1/8+1/9+1/10>1/10+1/10+1/10+1/10+1/10`

   `to B>5/10=1/2 \ \ (1)`

   $\\$

   `C=1/11+1/12+….+1/20`

   Có : 

   `1/11>1/20`

   `1/12>1/20`

   `….`

   `1/20=1/20`

   `to 1/11+1/12+….+1/20>1/20+1/20+…+1/20`

   `to C>10/20=1/2 \ \ (2)`

   Từ `(1)` và `(2) \ \ to A>1/2+1/2`

   `to A>1 \ \ (đpcm)`

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2. Ta có :

   `A = 1/6 + 1/7 + 1/8 +… + 1/20`
   `=> A = (1/6+1/7+1/8 + 1/9+1/10) + (1/11 + 1/12 +1/13+..+1/19+1/20)`
   Ta thấy  
   `1/6 > 1/10`
   `1/7 > 1/10`
   `1/8 > 1/10`
   `1/9 > 1/10`
   `1/10 = 1/10`
   `=> 1/6+1/7+1/8 + 1/9+1/10 > 1/10 + 1/10 + 1/10 + 1/10 +1/10`
   `=> 1/6+1/7+1/8 + 1/9+1/10 > 5 . 1/10`
   `=> 1/6+1/7+1/8 + 1/9+1/10 > 1/2 (1)`

   Ta thấy :

   `1/11 > 1/20`
   `1/12 > 1/20`
   `1/13 > 1/20`
   `…`
   `1/19 > 1/20`
   `1/20 = 1/20`
   `=> 1/11 + 1/12 +1/13+..+1/19+1/20 > 1/20 + 1/20 + 1/20 + …. + 1/20`
   `=> 1/11 + 1/12 +1/13+..+1/19+1/20 > 10. 1/20`
   `=> 1/11 + 1/12 +1/13+..+1/19+1/20 > 1/2 (2)`

   Từ `(1)` và `(2)` suy ra :

   `1/6+1/7+1/8 + 1/9+1/10 + 1/11 + 1/12 +1/13+..+1/19+1/20 > 1/2 + 1/2`

   `=> A > 1 (đpcm)`

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