Question

[Edokawa Conan]

B=1/4+1/5+1/6+...+1/19

Chứng minh rằng B>1

Answer 1

[Edokawa Conan]

Nhanh lm ơn!!

Answer 2

[๖²⁴ʱTú❄⁀ᶦᵈᵒᶫ]

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

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

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

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

\(\Rightarrowđpcm\)