Question

Chứng minh A>1/2

A=1/11+1/12+...+1/20

Answer 1

\(\frac{1}{11}>\frac{1}{20};\frac{1}{12}>\frac{1}{20};...;\frac{1}{20}=\frac{1}{20}\)

\(\Rightarrow A=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{10.1}{20}\)

\(\Rightarrow A>\frac{1}{2}\)

Chúc bạn học tốt^^

Answer 2

\(A=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)

                                                               10 phân số

\(A>10.\frac{1}{20}=\frac{1}{2}\left(đpcm\right)\)

Answer 3

\(\frac{1}{11}>\frac{1}{20};\frac{1}{12}>\frac{1}{20};...;\frac{1}{20}=\frac{1}{20}\)

\(\Rightarrow A=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{10.1}{20}\)

\(\Rightarrow A>\frac{1}{2}\)

Chúc bạn học tốt^^

Answer 4

Ta có : \(\frac{1}{11};\frac{1}{12};...;\frac{1}{20}>\frac{1}{20}\)

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)( 10 phân số 1/20 )

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{10}{20}\)

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{2}\)

\(\Rightarrow A>\frac{1}{2}\)