Question

cho S=1/31+1/32+1/33+...+1/60 chung minh 3/5 < S < 4/5

Answer 1

S = (1 / 31 + ... + 1 / 40) + (1 / 41 + ... + 1/ 50) + (1 / 51 + ... + 1 / 60) < 
10 / 31 + 10 / 41 + 10 / 51 < 10 / 30 + 10 / 40 + 10 / 50 = 1 / 3 + 1 / 4 + 1 / 5 = 
7 / 12 + 1 / 5 < 3 / 5 + 1 / 5 = 4 / 5 
Tương tự:
S > 10 / 40 + 10 / 50 + 10 / 60 = 1 / 4 + 1 / 5 + 1 / 6 = 5 / 12 + 1 / 5 > 2 / 5 + 1 / 5 = 3 / 5 
=> 3 / 5 < S < 4 / 5