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

Ta có :

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

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

Ta thấy :

\(\dfrac{1}{5}+\dfrac{1}{6}+\dfrac{1}{7}+\dfrac{1}{8}+\dfrac{1}{9}>\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}+\dfrac{1}{9}\)\(=\dfrac{1}{9}.5=\dfrac{5}{9}\)\(>\dfrac{1}{2}\)

\(\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}+......+\dfrac{1}{19}>\dfrac{1}{19}+\dfrac{1}{19}+.........+\dfrac{1}{19}\)\(=\dfrac{1}{19}.5=\dfrac{5}{19}\)\(>\dfrac{1}{2}\)

\(\Rightarrow B>\dfrac{1}{4}+\dfrac{1}{2}+\dfrac{1}{2}=\dfrac{5}{4}>1\)

\(\Rightarrow B>1\rightarrowđpcm\)

~ Chúc bn học tốt ~

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mình ko rảnh bn trả lời hộ mình luôn đi, mình tk cho

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)

đề là j vậy?