Question

Rút gọn

\(\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}......\frac{899}{30^2}\)

Hộ! 

Answer 1

Đặt \(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)

\(\Rightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{29.31}{30.30}\)

\(\Rightarrow A=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}\)

\(\Rightarrow A=\frac{\left(1.2.3...29\right).\left(3.4.5...31\right)}{\left(2.3.4...30\right).\left(2.3.4...30\right)}\)

\(\Rightarrow A=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)

Vậy \(A=\frac{31}{60}\)