Question

\(\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}\)

chứng minh S>1/3

mình cần gấp 

Answer 1

Ta có:

\(\frac{1}{12}>\frac{1}{20}\)

\(\frac{1}{13}>\frac{1}{20}\)

\(\frac{1}{14}>\frac{1}{20}\)

......

\(\frac{1}{19}>\frac{1}{20}\)

\(\Rightarrow\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}\)\(>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)

                                                                                                                   \(=\frac{8}{20}=\frac{2}{5}>\frac{1}{3}\)

\(\Rightarrow\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}+\frac{1}{17}+\frac{1}{18}+\frac{1}{19}>\frac{1}{3}\)