Question

cho B=1/4+1/5+1/6+...+1/19. Chung to rang B>1

MINH CAN GAP 

 

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Answer 1

ta có: \(\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{10}>\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}=\frac{7}{10}\)( có 7 số 1/10)

\(\frac{1}{11}+...+\frac{1}{19}>\frac{1}{19}+...+\frac{1}{19}=\frac{9}{19}\)( có 9 số 1/19)

\(\Rightarrow\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>\frac{7}{10}+\frac{9}{19}=1\frac{33}{190}>1\)

\(\Rightarrow B=\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{19}>1\left(đpcm\right)\)