Question

Cho \(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{99.100}\). CMR: \(\frac{7}{12}< A< \frac{5}{6}\)

Answer 1

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+............+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow A=1-\frac{1}{100}\)

\(\Rightarrow A=\frac{99}{100}\)

Vì \(\frac{7}{12}< \frac{99}{100}< \frac{5}{6}\Rightarrow\frac{7}{12}< A< \frac{5}{6}\)               ĐPCM

( Bài này ko ai lm thì t lm cho )