Question

Thực hiện phép tính \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{624}{625}\)

Answer 1

- Đặt \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{624}{625}\)

- Ta có: \(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{624}{625}\)

\(\Leftrightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{24.26}{25.25}\)

\(\Leftrightarrow A=\frac{1.2.3.....24}{2.3.4.....25}.\frac{3.4.5.....26}{2.3.4.....25}\)

\(\Leftrightarrow A=\frac{1}{25}.\frac{26}{2}\)

\(\Leftrightarrow A=\frac{1}{25}.13=\frac{13}{25}\)

Vậy \(A=\frac{13}{25}\)