Question

Cho M=\(\dfrac{5}{11}+\dfrac{5}{12}+\dfrac{5}{13}+\dfrac{5}{14}\). Chứng tỏ rằng 1 < M < 2

Answer 1

Ta xét:

`5/11 > 5/20`

`5/12 > 5/20`

`5/13 > 5/20`

`5/14 > 5/20`

`-> 5/11+5/12+5/13+5/14 > 5/20+5/20+5/20+5/20`

`=> 5/11+5/12+5/13+5/14 > 1 (1)`

Ta xét:

`5/11 < 5/10`

`5/12 < 5/10`

`5/13 < 5/10`

`5/14 < 5/10`

`-> 5/11+5/12+5/13+5/14 < 5/10+5/10+5/10+5/10`

`=> 5/11+5/12+5/13+5/14 < 2(2)`

Từ `(1),(2),` ta `-> 1 < M < 2`