Question

Chứng minh rằng :1/41+1/42+1/43+...+1/80 > 7/12

Answer 1

Ta có: 
7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80 
1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 = (1/41 + 1/42 + 1/43 + ...+ 1/60) + (1/61 + 1/62 +...+ 1/79 + 1/80) 
Do 1/41> 1/42 > 1/43 > ...>1/59 > 1/60 
=> (1/41 + 1/42 + 1/43 + ...+ 1/60) > 1/60 + ...+ 1/60 = 20/60 
và 1/61> 1/62> ... >1/79> 1/80 
=> (1/61 + 1/62 +...+ 1/79 + 1/80) > 1/80 + ...+ 1/80 = 20/80 
Vậy: 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 20/60 + 20/80 = 7/12 
=> 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 7/12 ( ĐPCM )