Question

A= 1/101+1/102+1/103+.....+1/200 cmr 7/12<A<1

Answer 1

\(A=\left(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{150}\right)+\left(\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}\right)\)

\(A>\left(\frac{1}{150}+\frac{1}{150}+...+\frac{1}{150}\right)+\left(\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}\right)\)

=> \(A>\frac{50}{150}+\frac{50}{200}=\frac{1}{3}+\frac{1}{4}=\frac{7}{12}\)

Lại có: \(A=\frac{1}{101}+\frac{1}{102}+...+\frac{1}{200}< \left(\frac{1}{100}+\frac{1}{100}+...+\frac{1}{100}\right)=\frac{100}{100}=1\)

=> \(\frac{7}{12}< A< 1\)