Question

Cho B = 1 / 4+ 1/5+1/6+....+1/19 

Hãy chứng minh B > 1

Answer 1

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