Nhok tham khao bai ben duoi i

Ta có B = 1/4 + 1/5 + 1/6+1/7+..+1/19

           >1/19+1/19+..+1/19

           =19/19=1

  Vậy B>1

\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)

\(\Rightarrow B>\frac{1}{4}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)(15 số hạng \(\frac{1}{20}\))

\(\Rightarrow B>\frac{1}{4}+\frac{1}{20}.15\)

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

Vậy B > 1 (đpcm)

Nhanh lm ơn!!

\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)

\(=\frac{1}{4}+\left(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}\right)+\left(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}\right)\)

Ta có : \(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}>\frac{1}{9}+\frac{1}{9}+...+\frac{1}{9}=\frac{1}{9}.5=\frac{5}{9}>\frac{1}{2}\)

\(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}>\frac{1}{19}+\frac{1}{19}+...+\frac{1}{19}=\frac{1}{19}.5=\frac{5}{19}>\frac{1}{2}\)

\(\Rightarrowđpcm\)

\(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}=\left(\frac{1}{4}+\frac{1}{5}+...+\frac{1}{11}\right)+\left(\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}\right)>\left(\frac{1}{11}+\frac{1}{11}+...+\frac{1}{11}\right)+\left(\frac{1}{19}+\frac{1}{19}+...+\frac{1}{19}\right)=\frac{8}{11}+\frac{8}{19}=\frac{240}{209}>\frac{209}{209}=1\Rightarrow B>1\)

\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}\)

\(B=\frac{1}{4}+\left(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}\right)+\left(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}\right)\)

\(\text{Mà:}\)\(\frac{1}{5}+\frac{1}{6}+...+1>\frac{1}{9}+\frac{1}{9}+...+\frac{1}{9}=\frac{5}{9}>\frac{1}{2}\)

\(\text{Mà:}\)\(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}>\frac{1}{19}+\frac{1}{19}+...+\frac{1}{19}=\frac{10}{19}>\frac{1}{2}\)

\(\text{Vậy:}\)\(B>1\)

\(B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+...+\frac{1}{16}=\frac{16}{16}=1\)

 =1/4 + (1/5 + 1/6 + 1/7 +1/8 + 1/9) + (1/10+1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19)

Vì 1/5 + .. + 1/9 > 1/9 +1/9 +1/9 + 1/9+1/9 Nên : 1/5 + .. +1/9 > 5/9 > 1/2

Vì 1/10 + 1/11 +... +1/19 > 1/19+1/19 + ... + 1/19 (có 10 số hạng) Nên : 1/10 + 1/11 +.. +1/19 > 10/19 > 1/2

=> B > 1/4 + 1/2 +1/2 > 1

=> B > 1

Vậy B > 1

Ủng hộ nghen

 =1/4 + (1/5 + 1/6 + 1/7 +1/8 + 1/9) + (1/10+1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19)

Vì 1/5 + .. + 1/9 > 1/9 +1/9 +1/9 + 1/9+1/9 Nên : 1/5 + .. +1/9 > 5/9 > 1/2

Vì 1/10 + 1/11 +... +1/19 > 1/19+1/19 + ... + 1/19 (có 10 số hạng) Nên : 1/10 + 1/11 +.. +1/19 > 10/19 > 1/2

=> B > 1/4 + 1/2 +1/2 > 1

=> B > 1

Vậy B > 1

Ủng hộ nghen

B= ( 1/4 + 1/5 + ... + 1/11 ) + ( 1/12 + 1/13 + ... + 1/19 ) > ( 1/11 + 1/11 + ... + 1/11 ) + ( 1/19 + 1/19 + ... + 1/19 ) = 8/11 + 8/19

B > 240/209

Suy ra B > 1 ( điều phải chứng minh ).