Question

Các bạn giải chi tiết giúp mình nha :)))

Answer 1

\(A=\dfrac{1}{2.3}+\dfrac{1}{4.5}+\dfrac{1}{6.7}+...+\dfrac{1}{18.19}\)

\(< \dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{17.18}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{17}-\dfrac{1}{18}\)

\(=\dfrac{1}{2}-\dfrac{1}{18}=\dfrac{4}{9}=\dfrac{76}{171}< \dfrac{9}{19}=\dfrac{81}{171}\)

\(\Rightarrow A< \dfrac{9}{19}\)