Question

Cho B= 1/4 + 1/5 + 1/6 + ... + 1/19. Hãy chứng tỏ rằng B>1

Answer 1

Xét: 1 / 4 > 1 / 16 ; 1 / 5 > 1 / 16 

=) 1 / 4 + 1 / 5 + 1 / 6 + ... + 1 / 19  > 16 . 1 / 16 = 16 /16 = 1

=) B > 1

Vậy B > 1

Answer 2

B= 1/4+(1/5+1/6+...+1/9)+(1/10+1/11+...+1/19)
Vì 1/5+1/6+...+1/9 > 1/9+1/9+...+1/9 nên 1/5+1/6+...+1/9 > 5/9 >1/2
Vì 1/10+1/11+...+1/19 > 1/19+1/19+...+1/19 nên 1/10+1/11+...+1/19 > 10/19 >1/2
Suy ra: B > 1/4+1/2+1/2 > 1