Question

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

 

Answer 1

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

Vì : \(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}>\frac{1}{9}+\frac{1}{9}+...+\frac{1}{9}\)nên \(\frac{1}{5}+\frac{1}{6}+...+\frac{1}{9}>\frac{5}{9}>\frac{1}{2}\)

Vì : \(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}>\frac{1}{19}+\frac{1}{19}+...+\frac{1}{19}\)nên \(\frac{1}{10}+\frac{1}{11}+...+\frac{1}{19}>\frac{10}{19}>\frac{1}{2}\)

\(\Rightarrow B< \frac{1}{4}+\frac{1}{2}+\frac{1}{2}>1\)

Answer 2

Bạn cứ so sánh với 1