Question

cho A=1\2+1\301+1\302+...+1\399+1\400 ,CMR A nhỏ hơn1

Answer 1

Ta có:

\(+)\frac{1}{301}>\frac{1}{300}\)

\(+)\frac{1}{302}< \frac{1}{300}\)

..................................

\(+)\frac{1}{400}< \frac{1}{300}\)

Suy ra \(\frac{1}{301}+\frac{1}{302}+...+\frac{1}{400}< \frac{1}{300}+\frac{1}{300}+...+\frac{1}{300}=\frac{1}{300}.100=\frac{1}{3}\)

\(\Rightarrow\frac{1}{2}+\frac{1}{301}+\frac{1}{302}+...+\frac{1}{400}< \frac{1}{2}+\frac{1}{3}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}< 1\)

hay \(A< 1\)

Vậy \(A< 1\)