Question

chứng tỏ: a, 1/5 + 1/6 + 1/7 + .... + 1/17 < 2

               b, 1/5 + 1/13 + 1/25 + 1/41 + 1/61 + 1/85 + 1/113 < 1/2

Answer 1

a, 1/5+1/6+1/7+1/8+1/9 < 1/5.5=1  ⁽¹⁾

    1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17 < 1/10.7 < 1/10.10 < 1  ⁽²⁾

    Từ (1) và (2) , suy ra 1/5+1/6+1/7+...+1/17 < 1+1 =2

Suy ra , 1/5+1/6+1/7+...+1/17 < 2

b, Ta cần c/m 1/13+1/25+1/41+1/61+1/85+1/113 < 3/10 (Vì 1/2 - 1/5 = 3/10)

                     1/13+1/25+1/41+1/61+1/85+1/113 < 1/10+1/25+1/25+1/25+1/25+1/25

                     1/13+1/25+1/41+1/61+1/85+1/113 < 1/10 + 5/25 = 1/10+1/5 = 3/10

Suy ra , 1/5+1/13+1/25+1/41+1/61+1/85+1/113 < 1/2