B=(1/4+1/5+1/6+1/7)+...+(1/16+1/17+1/18+1/19)

1/4+1/5+1/6+1/7>4*1/7=4/7

1/8+1/9+1/10+1/11>4*1/11=4/11

...

1/16+1/17+1/19+1/19>4/19

=>B>4(1/7+1/11+1/15+1/19)>1

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B=1/4+1/5+1/6+...+1/19

⇒B>1/4+1/19+1/19+1/19+...+1/19  có 15 số 1/19

⇒B>1/4+15.1/19

⇒B>1/4+15/19

⇒B>19/76+60/76

⇒B>79/76>1

⇒B>1 (đpcm)

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

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

Ta có : \(B=\frac{1}{4}+\left(\frac{1}{5}+\frac{1}{6}+....+\frac{1}{19}\right)>\frac{1}{4}+15\times\frac{1}{20}\)

  \(B>\frac{1}{4}+\frac{15}{20}=\frac{1}{4}+\frac{3}{4}=1\)

\(\Rightarrow B>1\)

B = 1/4 + 1/5 + 1/6 +....+1/19

> 1/4 + ( 1/20 + 1/20 +.....+1/20) ( 15 p/s 1/20) = 1/4 + 3/4 = 1

=> B > 1

Vậy B > 1