Question

[Công Chúa Nhật Kim Anh]

tính:

\(1\frac{1}{3}\) x   \(1\frac{1}{8}\) x  \(1\frac{1}{15}\) x   \(1\frac{1}{24}\) x ............x \(1\frac{1}{99}\)

Answer 1

[Đinh Đức Hùng]

\(1\frac{1}{3}.1\frac{1}{8}.1\frac{1}{15}.....1\frac{1}{99}\)

\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}......\frac{100}{99}\)

\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.....\frac{10.10}{9.11}\)

\(=\frac{\left(2.3.4...10\right)\left(2.3.4....10\right)}{\left(1.2.3...9\right)\left(3.4.5....11\right)}\)

\(=\frac{10.2}{11}=\frac{20}{11}\)