Question

Rút gọn biểu thức \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}....\frac{899}{900}\) ta được A=

Answer 1

Ta có: A=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}....\frac{899}{900}\)

\(\Leftrightarrow A=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}.\frac{4.6}{5^2}....\frac{29.31}{30^2}\)

\(\Leftrightarrow A=\frac{1.2.3.4...29}{2.3.4.5...30}.\frac{3.4.5.6...31}{2.3.4.5...30}\)

\(\Leftrightarrow A=\frac{1}{30}.\frac{31}{2}\)

\(\Leftrightarrow A=\frac{1.31}{30.2}\)

\(\Leftrightarrow A=\frac{31}{60}\)